Can a tourist purchase a car in the US and insure?

Wouldn't be a simple thing to do. The problem is that the car would have to be registered, and the person registering it would have to hold a drivers license in the state they're registering it in, and, in order to be eligible to get a drivers license here, they'd have to establish themselves as a resident of that state (in which case, they'd have to become a resident of the US, at which point, they cease to be a tourist).