> Serology is a thing, as are records of positive test results.

Serology is a thing, sure. But two points:

Getting a serum test rather than getting the vaccine is not going to be cheaper, easier, or better studied. We are not constrained on vaccine supply. So the practical advantage of allowing a totally different pathway is not obvious.

Creating another pathway adds a lot of cognitive load and confusion. The bar bouncer checking vaccination status at the door is not likely to know anything about serology. The same goes for people eager not to get Covid and the people eager not to accidentally kill grandma. Every bit of complexity is met with complaints and confusion; every change in regulation makes it harder for people to know what to do and therefore less likely to do it.

In some future pandemic might we want to create a two-pathway system? E.g., such that there's a government-issued "safe to mingle" digital passport? Sure. That seems like a great thing to start preparing now so it's ready the next time a disease hops the species barrier. For now, though, I think we should stick with the current plan: vaccination for (almost) everybody.