It's unlikely that would be sustainable for long for various reasons. You're talking about needing literally tens of BILLIONS of shots a year for the forseeable future?
If immunity is not long lasting, then the only path out is global eradication. We have done it before with smallpox.
I don't see us getting to the levels of vaccinations that would be necessary for eradication. A quarter of the people in the US think the whole thing is a ploy to implant everyone with microchips and nothing will ever convince them otherwise. Maybe some of those people will change their minds when they get it but I wouldn't count on enough to matter. We're all going to be sick and dying for decades.
Could they really manage to make a new version of the vaccine four times a year? For influenza they only do it twice a year and the vaccines are often only 50% effective (or worse.)
I would assume this is because of how fast flu is evolving and how many strains there are, with different ones predominant in any given year. Covid is (relatively) stable, so you'd just use the same one.
In the case of covid, the suspicion is that the former is true. There isn't enough data yet to be able to say one way or the other with any certainty, however.