Gun control mandates, and global warming mandates make sense to socialists. So do gender-neutral bathrooms. I don’t see any federal powers to mandate medical treatment in the Constitution. Moreover, informed consent to medical treatment is a foundation of ethics in medicine.
First of all the states mandate vaccines.
Secondly, it is a proven fact that when some people don’t get vaccinated it hurts herd immunity thereby threatening everyone.
So, in reality, the mandate is based in reason and science.