Define serious disease. Is mild or asymptotic Covid 19 a serious disease? The subject is Covid never going away. With 4 billion unvaccinated in the world and breakthrough cases very common, I don't see how anyone is surprised its still around here. In your "magical" scenario, yes, I believe there still would be major outbreaks in cases eventually. Because 5% more come in the next day. And the next. And the next....
ITT in the last 24 hours there is an article about Cornell shutting down its campus with 900 cases despite everyone on campus required to be vaccinated and wear masks. The NFL players are at 94% and the personnel at 100%, and there is a big outbreak this week. Thanks to the vaccines (and those groups' age and health) probably not a single one will be at risk. But still a "significant uptick."
Now, if we were 100% vaccinated, we probably would hardly test and we probably wouldn't know or care that Covid was still around. But like you said, that's "magical."