No, that is "more against" the application of the interstate commerce clause than the logic I outlined above as it de facto is a prohibition on travel and interstate commerce. This is also explicitly covered by the full faith and credit clause (https://en.wikipedia.org/wiki/Full_Faith_and_Credit_Clause, the thing I couldn't remember). It follows that states must recognize each other's vehicle registration, driver's licenses, and marriage licenses. It also sees use in chasing people across state lines for bogus tickets and for removing people's rights via protection orders. It lends itself to contradictory outcomes because it essentially says "all states are right."

If you were to instead ask "can you sell a vehicle that can't be registered" the answer is "yes." You can also make your own car and in so doing ignore most safety and emissions requirements.

There is a notable lack of small car manufacturers and a lack of case law on some of this. Some do mostly cosmetic work on existing models, and some sell "kits" and may help you assemble it "yourself" so as to qualify for a shopbuilt title.