I'd assume that a lot of it is the existing polarization over the issue. It's easier to lie and say you already had COVID, and there's a bunch of people who'd probably do so. (Plus a lot of people who don't even know they've already had COVID, because of asymptomatic cases.)

The state of medical records in the USA is... not great, so it's easier to show evidence of the vaccination that can at least theoretically be verified.

EDIT: man, the rapid-downvoting is even worse here than in the Apple CSAM threads. :D