That's not free choice, that's called arm twisting.
Why is it arm twisting? Government is tasked with public safety. What they need to do to ensure that is dependant on the risk to the public. If people choose not to get vaccinated, and as a result, Covid poses a public safety risk, government needs to takes steps to reduce the risk of continued spread. If people take steps on their own to keep the risks down, government can stay out of it.