Maybe, but I doubt it. It’s possible that partitioning would allow for divide and rule, but that will lead to a lot of direct governance from King’s Landing, and I’m not sure that the Iron Throne has the capacity to do that.
So the danger is that in trying to keep the Westerlands down, you’re creating only a “hollow strength” that will vanish once one house eventually reunites the others. Because the problem is that there aren’t much in the way of natural borders inside the Westerlands, so you’re going to get a lot of fighting over territory, and chances are someone will win.