Security for one. If they were given the same autonomy that they enjoy now why not? It'd tend to keep both Turkey and Iran at bay wouldn't you think?
Whats in it for Jordan? Kurdish oil? I doubt theyd get any. They didnt keep the West BAnk, I doubt they want a bunch or irascable Iraqis and non-Arab Kurds to complicate their monarchy. It would more than double their population and headaches