Good luck proving it without a paper trail, though, or if someone
not you has your credentials and you don't

But yeah, it mostly very rarely matters... right up until the point it does, which is generally half way up some tributary of shit creek. You're usually pretty fucked regardless by that point, so it's probably a bit of a wash in terms of effort to usefulness, I'unno.
Effects are worst on the transient and otherwise disconnected, unsurprisingly, who have trouble reliably proving they're themselves even when they're actually who they say they are. Ain't exactly got character witnesses anyone'll trust if you're never in one place long enough to build connections, or the only folks also around you are in similar positions. Gotta' screw over the already screwed somehow or another!
And, of course, gods save us from attempts to actually maybe
mitigate any of that, 'cause this is the US and we all know the GOP in particular would go out of their way to fuck that up :V
Just gotta' hold on and hope things don't get too omnifucked until maybe hopefully the younger generations can unfuck some of this mess. Just another few decades, ahaha