You also can't vaccinate everyone at once. Vaccinating the world inevitably takes years, not months.
That leaves a lot of room for mutations. I don't see logistically how you get over that, you just can't. It sounds good but I don't see the practical solutions.
(And then we haven't even talked about cross infection with animals, deers are now 80% infected or something with covid? What happens when they cross over back with some new variant?)