Matt loosing his identity has been done on paper. So it is possible. But a costume and secret identity are necessary, in my opinion. You loose all the aspect of the unknow bringing fear and respect. I removes lots of story possibilities.
And about DNA, DNA identity doesn't exist for everyone, but only specific people (criminals mostly), and they are private.
Also with a good suite and mask it is hard to have an AI find out who the person under is. And it's not like if everybody's shape, weight, height, face under are stored in databases and a computer can just go look it up.
Picture a random guy in New York and try to find his name, well good luck.
Then about seing him change, that is a possibility. But still not an easy one. Let's say you can see his face in the dark, afar on a roof top, or you loosing once he flees, how do you hope to find out who he is ?
I don't think, even with modern tech that it's a 100% possible to find out a superhero's secret identity.