Hey, and if it's such a great idea, let's make the military PX and Commissary sales to military and dependents subject to sales tax too! Whoopee, gotta squelch all that 'Legalized tax evasion!'
Any site that is doing that right now is acting illegally. Current federal law specifically forbids the practice you describe for any sales that have any part of the transaction outside of the state's borders. Since it's virtually impossible to have an internet transaction actually stay in the same country, much less the same state, this effectively never happens legally. L. L. Bean got their butts sued off over doing just this about twenty years ago.