It would be in much better interests of the Saudis to protect the Kurds, and supply them with the necessary support. The Kurds are targets of Turkey, Daesh, and the Iranians, and for that matter, the Russians, but for a much less degree of engagement.
Carving out a stable state of Kurdistan, composed of ethnic Kurds, from the territories of Turkey, Syria, Iraq and Iran, and including a corner of Azerbaijan, a former province of the old Soviet Union, would do much to stabilize a buffer state with highly motivated and fiercely independent population. True, most of the Kurds are Muslim, but they feel little brotherhood with either the Alawites of Syria or the Shi’a of Iran.
The Peshmerga is one of the best of guerrilla armies in the world, and organized on a national basis, they could be a potent force for throttling the ambitions of either the Iranians or Turkey.
Regardless of what the Kurds think they were promised, that ain't gonna happen, they need to face realpolitik and make terms for some degree of autonomy and protection from Turk invasion, under Syrian and Iraqi sovereignty.