Why? The government compels you to do all sorts of stuff.
It's like masks. You should be able to make laws that force people to wear masks if there is a deadly disease that will kill other people in large numbers, in my opinion. For those that argue about undue force, what about driver's licenses, taxes, health checks at restaurants, food inspection, building codes, rules on water lines, seat belts, etc? Seat belts mostly just affect people in the car, yet masking and cv19 affects others, so it should be an easier thing to understand the impact.
My guess is our tortured political situation convinces people that somehow the situation is different than these other things.
Forcing would be literally forcibly entering people's homes and testing or vaccinating them against their will, or jailing them or removing them from the country if they refuse. But you could disallow people from entering certain kinds of property or areas if they don't agree to show test results / vaccination status or take a temperature test or wear a mask.
Once a vaccine is officially approved and rolled out, I don't think vaccination should be mandatory for residents of the US, but I also don't think people should be allowed to enter my place of work or education if they aren't confirmed to be vaccinated.
Public health. Commonweal. Morality. Consideration for the disadvantaged.
It is in fact exactly like masks. You’re not forced to wear one unless you want to be around other people.