The unexamined assumption here is that a large military budget means that the Saudi army is effective and would be able to defeat ISIS. But there are several reasons to doubt this:
- The Saudi Army hasn’t done much fighting in living memory. Their last major war was in 1934.
- Most Arab countries have experienced coups. This gives the royal family of Saudi an incentive to keep their military weak.
- Arab society isn’t great at producing military forces.
Of course, Saudi could pay the expenses of a war against ISIS, effectively hiring the US to do it. But to require that would mean to admit we’re an empire that can tax the provinces.