Natural immunity wasn't allowed.
I’ll actually agree that by the time vaccine mandates were made the strains didn’t diverge that much and it should have been perfectly acceptable to show iron clad proof of prior infection as an alternative for vaccine proof (if I’m not wrong that was actually the case in some scenarios).
Right now the evidence that boosters are more than a little bit helpful is rather lacking.
I say this as someone that got the original strain and then delta - and both were quite serious. I remember at the time I got delta there was supposed to be about a 1% chance of me getting reinfected, though that study might have been pre-delta as I got it quite early.
Looking at your answers looks like you really don't have a clue, but the worst thing is you don't realize that you don't a have clue. Just like ChatGPT. You think it is intelligent, but it is not.