No, it's really not a bad analogy, Tipi. You're taking state reciprocity of accepting drivers' licenses for granted, but that's not federally mandated. (If it were an Article IV, Section I Constitution issue -- i.e the "Full Faith and Credit" bit", the states would also have to accept concealed weapons licenses from all other states as well.) There's something called the "Driver License Compact" which most states have joined. Mostly it's a matter of states wanting to avoid the hassle of having to certify all drivers and vehicles which enter their roads.
States could set up test stations for vehicles and drivers entering their borders, just as they set up truck weigh stations. My California-bought car has only had smog checks, not the safety checks required for a vehicle to be registered in Maine. Right now I could drive my car to Maine and operate it without having to prove it's safe (by Maine standards) to operate. Doesn't mean that situation, as a matter of law, will continue.