Why not?
The 10th Amendment.
It is the duty of the federal government to ensure life, liberty, and the pursuit of happiness is not invalidated.
No, it isn't. It's duty is to ensure no one is deprived of life, liberty, or property without due process.
And if a state has the power to ensure that the public is protected and healthy from a disease, then the federal government, which must manage trade and travel between states, can ensure the same as all states have interstate travel and trade.
And the federal government can make that argument in court, and they are likely going to lose.
I mean, Biden could just ban interstate travel if vaccines aren't a thing. But... This seems like a better choice.
Biden cannot ban interstate travel or trade. What are you even talking about?