The "right to travel" that is discussed in the Supreme Court cases is not a right to travel in the sense of a right to go from your house to the mall, but a right to move from state to state. There are three components to the right: (a) the right to enter one state & leave another; (b) the right to be treated as a welcome visitor rather than a hostile stranger; and (c) for those who want to become permanent residents, the right to be treated equally to native born citizens.
In fact, Saenz was a case that dealt with state restrictions on the amount of welfare that a new resident could receive. The court found that such a restriction was violative of the right to travel--this, of course, is a far cry from anything that has to do with highways.
I'm going to move to Mexico, renounce my citizenship, and come back. Illegal (oops, undocument) immigrants seem to have more rights when it comes to unquestioned travel these days.
You may still be expected to show ID but it doesn't even have to be genuine.