I am not convinced. Influenza has a pretty wide range, typically 12-52K a year (in the US). Doubling that top number would put it about 20% of the covid deaths we are seeing in 2021. Both diseases disproportionately punish people who are the least productive members of society (based on age alone); I don't think businesses are going to be volunteering to enforce mask mandates themselves. And the government is already showing considerably less enthusiasm than a year ago. Citizens are tiring of the masks, as evidenced by the waning compliance rate.

Vaccines, on the other hand, seem promising. Though the effective mutation rate seems quite a lot lower than influenza and there are good reasons to believe that the covid boosters will be considerably more durable than the original shots. If it really did come down to getting a booster every year, though, I think a lot of people would be okay with that if it meant no more attempts at lockdowns and mask mandates.