Not necessarily. The flu mutates substantially and often, and new subtypes keep popping up making a consistently effective vaccine elusive (flu shots are 10-60% effective each year based on our ability to guess which strains will dominate). There's no meaningful evidence indicating the same is true for COVID yet, so once we've all had it -- or a vaccine -- it could be over just like that, never to be heard from again. Unlike the flu. In the full course of time the flu may well prove to be much more dangerous.

Time will tell. Not saying one way or the other just that the worst case you've illustrated is far from a foregone conclusion.