It would still be a weak card at $2 per VP stack. Buying an Estate early would still make no sense (since it's a shared thing, you'd be taking on an extra Estate, which is really bad, and your opponent could start adding Trade Route's to reap the benefit).
And it would have to wait until the dying moments of the game to be worth much, and even then how often are more piles than just Province are bought early enough to meaningfully add $2-$4 terminal compulsive trashers to your deck in the late game? Sure, it could be a lot of points in a game with like, Silk Road and Harem, but that's a very specialized case and also the time when terminal compulsive trashers are at their weakest (slogs).
So sure, you could make it worth $6 in every game, but I don't think you would because doing so wouldn't really give you any real advantage unless your opponent is a complete ninny.