That's not 100% true; boosters for the flu do not need to go through the whole 6-month-testing double-blind rigamarole. A COVID booster with a tweaked Delta specific formula could be approved much more quickly than the original vaccine. There's precedent for that.
Pfizer is testing a Delta-specific booster [1]. They can’t just plop it into the market. It has to go through a whole new set of approvals.
[1] https://cdn.pfizer.com/pfizercom/2021-07/Delta_Variant_Study...