Plagues end quickly all the time once conditions are no longer able to support it. Take a look at the current mouse plague in eastern Australia right now for a real world example. It's happened before but each time it collapsed as quickly as it came.
Statistically we will cross the threshold where the ecosystem is no longer favorable for the spread of covid and the plague will collapse. It will move back into the background noise just like the millions of other potential diseases that aren't currently causing a global pandemic.
The real danger are holdouts who can't or refuse to get vaccinated for whatever reason. If there's enough of them and they live close enough together to support a viable ecosystem that very well could provide a reservoir for covid to continue thriving and causing problems until they achieve herd immunity.
I can see several ways in which this is not true.
For one, several different variants might need to be handled with several different vaccines. Vaccines might also not work perfectly on a variant, but they might confer some protection, leading to overall less total viral particles produced, reducing the probability of an effective mutation.
Aren’t you committing a logical error here? There will need to be new vaccines as long as there is at least one escape variant. The “fewer the need” is really a binary 0 or 1, and you haven’t done anything to show that your “getting vaccinated and retaining some discipline until the collapse” gets us from a 1 to a 0. There’s a time component as well.
But yeah, it’s a neat story that gets shots in arms.