I’m technically identifiable by holding the button on my watch or the medical id button on my watch. I’m just not legally identifiable.
And really, who’s going to know (how) to do that, especially in an emergency? It also relies on either your phone or watch surviving an accident intact. It’s your life, but it’s just going to frustrate identification attempts when it’s important.
A wallet doesn’t have to be bulky a to hold a couple of cards or a few slips of paper. I have a cardholder which is much more minimal and compact than a standard wallet, and even Apple makes cardholders that attach to the back of MagSafe phones now.
When my phone was lost once, it was dropped off at the police station and they opened the emergency access screen to call someone to get the phone returned. So it’s not completely unknown.