You know that bit at the end of Iron Man where Tony Stark has been briefed with a secret identity cover story and then just says “I am Iron Man.” It was a pretty big surprise at the time, as secret identities are pretty standard operating procedure for superheroes and this had carried over into previous movies. The Marvel Cinematic Universe has largely followed Tony’s example and gone for public identities, apart from those actively working covertly and the Hulk. Note all the unmasked faces.
In the modern age of surveillance a secret identity would be hard to maintain without some hacking and trickery. This is how Finch and Reese operate in Person Of Interest.
Or would Batman just post his work on Facebook?
For modern melee armour, see also these guys who look like obscure 90s Marvel Night Thrasher.
(For my 1337th post, ninjas seem appropriate.)