On one hand, there are the fans who are enjoying the return of these classic characters, myself being one of them, and, on the other, there are fans of the legacy characters who are being replaced by these classic predecessors.
While some fans of the legacy characters from the past couple decades, such as Batgirl (Cassandra Cain), Green Arrow (Connor Hawk) and Supergirl (Linda Danvers), would like to have people believe this is because certain writers, most often citing Geoff Johns and Grant Morrison, are simply "Silver Age Fanboys" bringing the characters they grew up reading back, it is actually the symptoms of a much deeper problem that has plagued DC since the end of the Silver Age and Crisis on Infinite Earths.
For the purposes of this post, I'm going to divide DC's characters into four "waves". The first wave represents the classic Golden Age characters, such as Earth-2 Superman and members of the JSA (Alan Scott, Jay Garrick, and Ted Grant).
The second wave of characters were the ones that came in with the Silver Age, characters such as Hal Jordan and Barry Allen.
The third wave begins with the post-Crisis on Infinite Earths characters, like Superboy (Kon-El), Batgirl (Cassandra Cain), Green Arrow (Connor Hawke), Green Lantern (Kyle Rayner) and Impulse (Bart Allen, who later became Flash). Although Wally West is technically from the second wave, where he was Kid Flash, I'm putting him with this wave since this around the time when he become the Flash.
The fourth and final wave are the newest round of legacy characters, plus a few new ones, such as Manhunter (Kate Spenser), Blue Beetle (Jaime Reyes), Batwoman (Kate Kane), the Atom (Ryan Choi), and Firestorm (Jason Rusch).
Although Barry Allen and Hal Jordan are the original legacy characters, they are not the origin of DC's problems when it comes to multiple people sharing the same super hero identity. Both Jordan and Allen can and did exist completely separate from Alan Scott and Jay Garrick, since Scott and Garrick were both from different times and, in the books themselves, different realities.
In actuality, Wally West can be considered the original forerunner for all legacy characters running around the DC Universe, which compose my "third wave". He replaced his predecessor from the same reality, unlike Hal and Barry's replacement of WWII heroes from alternate Earths, and had known and served as a sidekick of Barry.
This was what made the third wave of characters different from the second - they existed in the same reality as the their predecessors and eventually took up their mantles, unlike the second wave's reusing of concepts established back in the 30's.
This brings them into conflict among fans over who's the better or 'true' character in a way that the introduction of Barry and Hal did not have on the pre-existing Jay and Alan. In the case of these legacies, you typically have to get rid of one in order to get the new version. This has had the obvious problems of upsetting one group of fans when their favorite character is now second to another character that is either the Legacy character or their predecessor.
The Origin Problem
Another problem facing legacy characters is that, outside of the first wave of legacy characters, they don't usually have independent origins. While this isn't so much of a problem with regular readers, it is a problem for attracting new readers.
For example, Kyle Rayner and Wally West don't have independent origins. They are directly linked to their predecessors, Hal Jordan and Barry Allen's removal/deaths. Hal become Parallax which led to Ganthet, the last Guardian, making Kyle the last Green Lantern while Barry died back in CoIE.
Barry and Hal, as second wave characters, have truly independent origins from their first wave countparts while Wally and Kyle "need" Barry and Hal as the catalyst for their existence as characters. Looking at it objectively, Hal and Barry are "better" characters than either Kyle or Wally because of this.
For a simple example of this, in Justice League Unlimited, the Flash was Wally's personality with Barry's origin and history. This applies to several other legacy characters featured in the DC animated universe. It's a glaring flaw in many otherwise solid characters.
This all begs the question, why is DC bringing back these specific legacy characters in the first place? After all, in reference to Barry or Wally and Hal or Kyle, many people in the public probably don't even know one of these characters from the other despite many knowing who Flash or Green Lantern are.
Look at Batman the Animated Series and, by extension, the rest of the DCAU. Many of the second wave characters appeared in either Batman, Superman or Justice League. Both Batgirl and Supergirl appeared in the series, but not as the "fan favorite" versions that first appeared post-Crisis (ie, neither Cassandra Cain nor Matrix/Linda Danvers versions appeared). In the Batgirl's case, it was the Barbara Gordon version featured in Batman: TAS and, again, in The Batman. When it came to Supergirl, she was Superman's "cousin", alla the Silver Age.
By using these characters in television, these are the versions that people are going to be most familiar with. One of the hoped for side effects of doing things like TV shows is to get more people to read comics. If a person's favorite character from the show isn't in the comics ,then DC has more than likely lost or alienated a customer.
This is why Cassandra Cain, Linda Danvers and most of DC's legacy characters are not the best possible versions of these characters - they simply don't match what the public perceives Batgirl and Supergirl, or anyone else, should be, which isn't good for DC's comic versions either.
So, why not make the animated versions match up with the most recent versions? Well, sometimes the newest legacy character appeared after the TV show aired(Cassandra Cain) or their origins are too complicated(Matrix/Danvers Supergirl) and this basically means that the creation of a third version or hybrid of Silver Age and modern versions of the character would be necessary.
The question of who is better, Marvel or DC, will rage forever without a definitive answer, but one thing is pretty certain, - Marvel's characters are simply more stable than DC's.
While the A-listers at both companies are pretty much set in stone, even Marvel's lower tier characters are fairly stable compared to the numerous waves of DC legacy changes that take place.
Despite the fact that DC characters are generally viewed as "icons", there are still a lot of characters that share the names and mantles across different mediums, from televison to toys to movies. In Marvel's case, the fact is, if you see or like a Marvel character from another media, odds are their comic book counterpart is basically the same, even when it comes to the B and C-list characters. The odd exception to this was with the always single portrayal of Spider-Man, but One More Day changed that.
As a quick aside about OMD, in just about every non-comic Spider-Man property it is strongly hinted at that Spidey and Mary Jane would either get together or eventually get married. Undoing the marriage in the comic actually creates a difference between the two when Quesada was actually trying to align them. Now, that's not the only, or main, reason why he did it, but it is there.
This is one of the things that has hampered many of the third wave Legacy characters. They got started in a time of upheavals in both the DCU and the comics industry. Even if they had managed to catch on, they never reached the necessary acceptance level to thrive as many of the second wave characters did. This also decreased the likelihood of the them appearing in other media, which would have cemented their claim to their legacy mantle.
The Few Survivors
Despite the failure of many third wave legacy characters to catch on, two have managed to do surprising well - Wally West and Kyle Rayner - but for different, yet very important reasons.
In Wally's case, unlike just about every other third wave legacy character, Wally made it to "Icon" status. The Flash is one of the seven founding members of the JLA which made Wally a lot more visible, especially when it came to other media like JLU. He also had the longest time to establish himself, some 20 years before Barry Allen finally came back. In addition, he had two definitive back-to-back runs by Mark Waid and Geoff Johns, which really helped to firmly establish him both with fans and within the DCU. Wally has "made it" in every sense of the phrase.
Kyle Rayner is the second legacy character to survive his predecessor's return and has done better that most other Legacy characters for very different reasons than Wally's. First and foremost, Kyle is part of the Green Lantern Corps. There has almost always been multiple Green Lanterns, especially in regards to Earth based versions, which has allowed him to stick around after Hal's return. Ironically, the one exception to this 'multiple GL' rule was when Kyle was first introduced. Either way, this meant that Kyle went from being The One to being One Among Many. This is something that many Legacy characters don't have the chance to do.
He also had an in-story reason to stay prominent - he was the Torchbearer, the man who kept the GLC going when everyone else was gone. Again, very few Legacy characters have had in-story reasons for them to remain prominent after their predecessors have returned. So, while Wally and Kyle are indeed the exceptions to the legacy character rule, they also prove just how hard it is to pull off and stay relevant.
The Next Wave
Jaime Reyes, the current Blue Beetle, is probably the perfect legacy character. His origin is connected to his predecessor yet independent, Jaime found the scarab which attached itself to him and made him the Blue Beetle.
But, more importantly, his history as a character also has something that distinguishes him from many of the other legacy characters - a TV show. While not specifically a Blue Beetle show, he has appeared on Batman: The Brave and The Bold twice.
This is one reason why he will probably succeed where so many others have failed - mainstream exposure. Jaime Reyes is now the Blue Beetle that people outside comics will know about and if they get the urge to check his comic book adventures, he will be there as well.
This also applies to a lot the of the fourth wave legacy characters. It is more likely that they will have opportunities to appear in outside media than previous characters increasing their chances of survival as long term characters in the DCU.
What Does It All Mean?
Basically, DC is undoing something that should have never really been done in the first place. This is not to say that any DC's legacy characters are mistakes, but, rather, they should have never eclipsed their predecessors in comics only. Many of them never made it into the public consciousness, which means they could never be as successful as the originals. Even among comic readers, Barbara Gordon is more likely to be know as Batgirl than Cassandra Cain.
What DC is doing is trying their best to make their characters have the greatest appeal possible and you do this by going with the characters people know the best. Regardless of Cassandra Cain's or Barbara Gordan's qualities as characters, Barbara is always going to be the better Batgirl since that is who most people know to be the character, which is why she should be Batgirl, at least in DC's eyes. Until DC decides on the wholesale evolution of all of it's characters, it is perhaps in their best interest to stick with what people know.