Well, it really depends on the timeframe. If we need a new one every two years, no problem. If every six months, that’s worse.
Current flu vaccine coverage is 24-50% depending on jurisdiction, once per year. So, aiming at, say, 80% coverage twice per year would be 3-6x the current level of flu vaccination effort.
You don't need 80% coverage though. Influenza would be a pandemic too (and has been!) but is well controlled by the existing regimes. There's nothing all that notable about covid really, beyond its novelty. Once the bulk of the population has some immunity, even if incomplete and even if it needs a regular refresh, we hit herd immunity: R0 drops below 1 and the disease stops spreading. There's no reason to expect this to work any differently.
Current flu vaccine coverage is 24-50% depending on jurisdiction, once per year. So, aiming at, say, 80% coverage twice per year would be 3-6x the current level of flu vaccination effort.
Not awful, but tiresome.