It's still pretty important in the DC universe. They've made the importance of secret identities and the consequences of the true identity of a hero a major point in several stories in the last decade. Now, not all of these stories were good, but that is another debate.
I think for the characters it still is important. Imagine if Batman's secret identity was public knowledge, it would take a lot of the mystique of the character away, even for readers.
Superman recently revealed his identity to the public in the comics, and already there are ramifications to that step. I fully expect that development to be retconned with the end of Bendis' run at the latest.
Over at Marvel, Spider-Man's identity being a secret is also a pretty important part of the character, the comics showed the personal catastrophe this would have in the aftermath of Civil War, and it was retconned pretty quickly (and with that intention from the very start, so it was more of a semi-reset button than a retcon.
Now, with the reality of governments and big tech using technology to learn (not necessarily publicly reveal, mind you) the true identity of superheroes, this has been used as story points, as well. Amanda Waller has been shown in "Justice League Unlimited" and the "Suicide Squad" movie to know the true identity of Batman, but keeping it to herself.
But even there, there are narrative ways to work around that, mostly organized heroes with their own resources
Even in reality, facial recognition is far from foolproof, even without masks. There are simply too many people that have similar facial structure. That's something that always bugged me about the "Superman only uses glasses as a disguise" complaint. So Clark Kent and Superman look alike, so what, so must dozens of other men in Metropolis alone.
Aside from that, Justice League-distributed (or Avengers-, in case of Marvel) tech could be used to narratively counter that technology. Special masks simulating different facial structure, apps to fool trackers in other apps for their smartphones, (you want to track me via my phone? What if my phone gives you the wrong GPS signal), and that's not even the usefulness of shapeshifting heroes in the community. At the end of the "Death & Return of Superman" saga in the comics, Matrix-Supergirl pretended to be Superman to publicly find a surviving Clark Kent under the rubble left from the Doomsday battle (or she pretended to be Clark, I can't remember right now). Something like that would throw off a lot of intelligence services, whether state or private.
