Prevent the Andal Conquest of the Vale, I’m afraid.
The major difference between the mountain clans of the Vale and the hill clans of the North is that the former were driven into the mountains by a victorious invading people and the latter weren’t. Now compound that sense of grievance – the killings, the forced conversions, the seizure of land at swordpoint – over thousands and thousands of years.
Now, you might point to Jon Snow and Stannis trying to assimilate the wildlings into the North, and fair enough. However, there’s no Gift in the Vale to be given away as reparations/a place in the feudal order, there’s certainly no urgency among the mountain clans about the need to find safety within another society in the same way that the wildings want to get south of the Wall, and…well, how well is the assimilation of the wildlings going?
Let’s ask Lord Commander Jon Snow.

What’s that you say? Attempts to assimilate a long-hated minority led to a revanchist coup? Or has Olly fallen down the well?