Yes, and it may not be the ideal policy.

It may be better to do what we do with the flu, reevaluate the vaccine from time to time, and give the new version to everybody.

But also, around here covid seems to be a smaller problem than influenza, by a rate of 2 if you count only deaths. So it's understandable why people don't want to mess with it.

Where in the world do they give the flu vaccine to everyone?

Which is what is currently being done in many parts of the world.