The commerce clause cannot be used to abrogate fundamental individual rights, people are seriously misunderstanding what can be done under that clause. There is a mountain of Supreme Court precedent that covers this explicitly, and the specific case of freedom of travel, and also covers attempts to use regulatory technicalities to do the same. The right of Americans to travel freely absent narrow circumstances requiring due process is settled law at this point. This may be inconvenient for anyone that wants to implement a lockdown but this is well-trod legal territory.

I think people are also conflating what the Federal government can do, which is very little, and what local governments can do, which is considerably more. Broadly speaking, the Federal government operates in an "advise and support" role, the legal authority resides with the States and localities. This is an example of where State sovereignty becomes very obvious. But even with the States exercising their broader powers, they are still restricted from violating fundamental Constitutional rights like freedom of speech, assembly, travel, etc.