They should already know. Flu vaccines get updated every year, and we’ve known COVID immunity falls off fairly rapidly regardless. People were going only 3-6 months between infections in the initial outbreak. I don’t know what the longevity of the COVID vaccines are but it doesn’t seem great, even ignoring that you need updates for new mutations.
Now, maybe his supply of vaccine doesn’t protect against the latest strains, but if that was the case I’d expect him to have mentioned that, because it isn’t the overall supply either since some places are throwing them away.
There’s always the chance your doctor is just an idiot.
After all, do you know what you call the bottom 10% of a medical school graduating class?