False equivalence. For many reasons, not the least of which is that you are discussing property rights in the example and the use of said property on public routes.
But one does not NEED a car to move around as long as one has the ability to move about naturally. Thus I do not NEED a license unless I wish to drive a car.
Now explain how I NEED a "mask" or a "vaccine" if I am immune, or have a strong immune system so I suffer mildly, or I don't give a damn if I live or die via getting this disease?
You brought up clothing, and I refuted the value of that example.
The government should not "mandate wearing clothes" IMO, although common sense and human experience should teach someone that clothing protects from weather and other hindrances in a society. But we have many examples around the world of cultures which either have no, or limited "clothing requirements" and do just fine.
But I still reject the argument on the principle that clothing is more a custom of "polite" society out of cultural concerns over emotional reactions to the naked body. In any case it is still "expression" as one could wear shorts or a bathing suit all day perfectly legally. It would be up to private citizens, exercising their own property rights, to say whether that was sufficient to enter their abode or places of business.
Which leads me to the point that private citizens can always "regulate" whom to encounter, let on their property, and what is needed to engage with them. One is always free to limit oneself. The problem is allowing government to do so in more and more ways until one becomes the servant of those who govern, and not vice versa.