1) Ego
2) I have no scientific evidence for this but it feels humans want to confess and unless death find them first everyone will confess every crime they have done. It could be through a joke, or to a complete stranger or some other way.
Assuming they could identify him from camera footage, he'd have limited options to keep an existing car or buy a car and stay in the US? It'd be a risk even buying a car in a friend's name.
Best bet might be to forgo a car, rent somewhere remote and informally with cash, and sit tight for a while.
Drove over in a camper van with European plates, didn't even realise had left the US until got to the Mexican side and went and sorted papers for the vehicle. No search, no check, just passports
I've been to Mexico dozens of times and only once was anything checked at all.
I'm pretty sure his Russian gold fence could have set him up with bitcoin instead of cash in the first place, though.
I can only speak from personal experience, but ...
As someone who has driven into, and through, Mexico many, many times (one trip was Colorado to El Salvador and back) I can tell you that it's all smiles and waves and thumbs up as long as you are driving south.
As long as you're driving south, nobody cares what you're doing or what's up or where you're going or who you are.
The moment you turn around and point north everyone cares.
Or, as I said, get to a more remote area, make friends, rent a room cheap, befriend the landlord and try to borrow their car for cash, and then slowly develop a lifestyle where you can make careful use of the money without divulging your identity too much.
You wonder why the guy would not handle himself better? Well, if he was smart, then he would never think of it. He has access to the US and countless opportunities. He'd have been probably better off financially.
And he has access to NYC, he doesn't need a girlfriend.