This comes from my own personal history with comics. I read some Golden Age stuff, but stopped reading in 1976, during the Silver Age. I began again in 2000, so the changes were huge.
There are many reasons why costumed heroes wear a costume. They want some privacy. They want to have some semblance of a normal life. They want to protect their families and loved ones. They want to earn a living. They're doing something outside the law and will lose their freedom to act if it is known who they are.
Wonder Woman needed none of those things, but she was given one anyway because a hero has one, and in this case she got to be with the man she loved.
This need to have and protect a secret identity had a tremendous effect on the stories. They had to lie to their friends, coworkers and lovers. Lois dated Superman, not Clark; Steve Trevor dated Wonder Woman, not his dowdy secretary Diana Prince. And Bruce dated Selina, not Batman. Bruce always has to be different.
And then there are their relationships with other heroes. If they made the effort to keep their secrets - well, the other heroes wouldn't pry, although one can be sure that Batman knew anyway. But it meant that they had to put their lives in the hands of someone they don't actually know.
Even if they did know - they're friends or partners or even lovers, once they were in costume, they only used hero names. And when I watched or read these things as a kid, that seemed normal - that even in the Batcave, they would be Batman and Robin, or that Green Arrow would call his ladylove "Canary", not Dinah.
This created the impression that the people in the costumes were somehow different than the people outside them. More than that - the feeling was that the costume was the real identity, and the regular one was the disguise. This was heightened somewhat for the big three, as this was at the time the truth. Wonder Woman was the Amazon Princess, Superman was the alien, and Batman was...well. He did warp Bruce so no one would suspect the airhead playboy haunted the night.
And then we had the exceptions. Ralph Dibny, the Elongated Man never wore a mask or hid who he was. His wife Sue was a full partner. And this was shocking and strange. And in the 30th Century, the kids in the Legion of Super-Heroes sometimes used each others real names and never wore masks or kept who they were a secret. I remember loving this. It made them feel more like people.
I stopped reading comics for a quarter of a century. It wasn't purely by choice - they were getting costly ($0.33 an issue! Ate up a good chunk of my allowance.) and we moved to the suburbs. I didn't start again until 2000, and there were so many changes in that time - storylines, artwork, characterizations. If I hadn't read a few trades along the way and just heard things, I'd have been totally lost. As it was, I spent a lot time and money just getting caught up.
The attitude towards secret identities was one of the changes. I can point to various reasons, although I think many down to Crisis on Infinite Earths.
Before Crisis, there tended to be one superhero per name per Earth. The only exceptions were Green Lanterns, but there was a whole corps of them out there, so a couple of spares on Earth-1 weren't a problem, and Robins, but there was only one at a time.
After Crisis, the Golden Age versions of the heroes shared the same timeline as the Silver/Modern Age ones. We had two different Green Lanterns with different sources and weaknesses; we had three Flashes because Barry Allen has never lost his presence even though they have the grace to keep him dead. We had mantles passing from one hero to another. Once that happened, the person in the costume became more important than the costume itself.
Not only do we have two living and one dead Flash and several Green Lanterns, we have two Green Arrows, and frankly I'm not sure if they have any secrets - Ollie's goatee is pretty distinctive, as Connor's coloration, and Roy Harper is out anyway. We also have the memories of three - no, four - Robins and the wonderful and varied Starman legacy.
So it's no wonder we're seeing more first names - it's a lot less confusing. And as we're seeing them in a context of legacy and family, we're seeing them as more human who happen to wear costumes and have powers, training or toys.
One of the biggest changes is to the perception of Superman vs. Clark Kent. The TV series said, "And who, disguised as Clark Kent, mild-mannered reporter..." which says that Superman was the real identity. Clark's glasses and suits were the mask and costumes. He's Kal-El of Krypton, strange visitor, not one of us at all.
That's not what we see anymore. That even felt wrong to write. Thanks to John Byrne and the 90s series Lois and Clark and the current series Smallville, we see the son of Jonathan and Martha Kent, who may not be human and who may not have been conceived on Earth, but he is no "visitor." And he is the reporter, the award winning journalist and novelist. He's the husband of Lois Lane. Clark Kent is real. Kal-El? That's his Kryptonian name. He's proud of his heritage as anyone should be, but it's not him.
And he takes off his glasses and suits and dresses up as Superman. But Superman is not who he is.
And then there are the heroes who put on costumes and maybe masks or wigs and even use hero names but who make no effort to keep anything a secret.
Some don't have a reason - Diana has been retconned into arriving with full fanfare as a Princess and an Ambassador. She's not about to take a job just to pine over a man. Others can't hide - Argent has silver skin, Metamorpho has multimaterial skin. Jade is green, and while she can hide it, she doesn't.
Some seem to have given up hiding. Of the former Teen Titans, kids who grew up as heroes, only Dick Grayson remained behind a mask until Wally West made a wish to be forgotten. Some were outed - Cassie Sandsmark, the current Wonder Girl, had to save people at her school.
And then there's Jack Knight. He's the son of Ted Knight, the first Starman, and everyone knew both facts. So, when he decided to become Starman himself, after his brother was killed, Jack did it his way. His "costume" was whatever he put on that morning, a vintage leather jacket and a pair of goggles. No masks, no tights, no capes.
I honestly was wondering what the future of the secret identity was - it seemed more and more irrelevant. Having two became a liability a couple of years ago when the JLA was forcibly split - and it was the unpowered "real" selves who saved the day.
Only Batman and Superman seemed to be taking any care, and Superman seemed to relying on the impression that he was always Superman all the time, just like Wonder Woman.
Except, a year or so ago, Wally West made that wish and now he has a secret identity again. And this year's big event, Identity Crisis, is all about this concept.
It looked like Sue was killed because Ralph was out; we saw the lengths they went to protect their secrets; and we saw how precarious it all was - how a former family member who knew it all could endanger them all.
The secret identity gives the hero downtime. It protects his/her loved ones. It enables the hero to have a life and a job. It means that the hero can to his/her vigilante work. It's also a secret that must be kept, sometimes at a high cost, and a liability. They promise that the events of Identity Crisis will have effects all over the DCverse, beyond the losses of Sue Dibny, Jack Drake and Jean Loring. I hope so. It needs to be done.