There are points on both sides of the secret identity question.
Personally, I do miss them. I do think it "shrinks" a character's environment to be a celebrity, and closes off some kinds of access to some kinds of stories.
On the other hand, there are some characters that are absolutely supposed to be celebrities (i.e. The Fantastic Four). Further, technology has made it a lot harder to believe that somebody can get away with a disguise than it was in 1963. I also suspect that it reflects the more narcissistic society in which we live ("of course they're out in the open," says the writer, "nobody wants to project themselves onto an anonymous nobody!").
Big Two Comics aren't written for kids anymore, and that's where secret identities had their most power. The trope displays a character whose true potential isn't fully understood by those around them, who is secretly special (with an element of mocking the surrounding ignorants). It was designed to resonate with children who wanted the security of their regular lives, but aspired to be more (IMO, this is why the original Captain Marvel has never recaptured his initial popularity over the last 30 years; that concept is
pure child wish fulfillment...but, I digress).
Secret ids are a good fit for some characters, particularly the dark vigilante types, but writers need to apply some common sense.
- There's no point in having a secret identity unless there's some reason to maintain one (vulnerable loved ones, activities that are as likely to piss off the cops as the crooks, viciously vindictive enemies, etc.), and those reasons need to be a consistent element of the character's story (which is not to say they have to constantly be at the center of the character's story).
- Characters with secret ids shouldn't let themselves get photographed unless they've got full covering costumes, ala Spider-Man or Iron Man, or their costume includes some kind of radical body transformation, like The Hulk or Ant-Man.
- It's tempting for a creator to portray a superhero in costume as much as possible; that makes no sense for a character with a secret id (it's one of the things that I liked about Moon Knight's concept, even if they didn't always use them this way, his Lockley and Spector aliases provide him with a discrete means of doing his work, saving MK for when it's time to bust heads).
- It's absolutely insane for a character with a secret id to carry around a commercial cellphone "on the job", and certainly not a smartphone.
- A character with a secret id has got to have some regularly and explicitly depicted means of evading modern surveillance technology (be it a secret tunnel home, or teleportation abilities).
So, while I like the old secret id trope, it's not for everybody, and it's got to be used smartly for the ones it does work for.