Check turn, raise river, in position, in WA/WB problems

During lunch I was thinking about the WA/WB problem. A standard play seems to be checking the turn and calling the river when villain bets. What do you think of a standard play where instead, you always check the turn but raise the river?

My thinking is that on the river, it is quite rare that you will get 3-bet by anything other than a nut hand or a completed draw. Better hands will just call. However, weaker hands will also call, unless they are total bluffs.

That final bet will only get called by a better range of hands, hands that you may not fair as well against. And being 3-bet would be horrible. You will probably get 3-bet by hands that beat you much more than hands that you beat will call your raise, especially as you move up in limits.