"Friendly Arab Country" now there's a contradiction in terms. You might recall Saudi Arabia kicked us out (yeah I know we still have some stuff there, but 99% is gone).
More to the point, I think the idea is to stand up their military as a self sufficient force which by definition would mean they'd have to be in their out country.
Plus, any arab country safe enough to host such a base is still a damn sight better than Iraq so I don't think it would solve the AWOL/desertion rate much.