Actually, Saudi Arabia might get involved.
The coordination will be difficult (I doubt the Saudis are properly, NATO - style, trained for joint actions with USA).
Their involvement would also severely raise the risk of friendly fire (see the F15's over Kuwait).
My experience while working there years ago was that their armed forces were a weird mix of coup proofing and a nepotistic dumping ground for family members who couldn’t be trusted to help run the family business.
they can just pay gurkha mercenaries for the job