On the surface I would agree with you Altair, BUT...
1. Turkey - Yes, a NATO country. But not exactly the popular kid in the room. Historically, it made sense to have Turkey as an ally. Geographically close to multiple flashpoints, historically at odds with Russia.
Turkey's President seems quite happy to shun NATO as a partner. Mass detentions of anybody he wants, including judges, lawyers, teachers, students, soldiers, prosecutors, news reports, etc etc. Now purchasing AA gear from Russia, and openly attacking groups that other Western countries support. Not to mention, fairly extreme in his political views...don't think this is lost on NATO leadership.
2. Russia - I don't think Russia cares that much. If the Kurds can offer relative stability to the region, decent professionalism, no mass genocides, etc etc - it's preferable to the other groups. Plus they know that on SOME LEVEL, they do enjoy the support of the West, albeit how much support seems to change frequently.
3. Syria - Lots of it's own problems to deal with. Attacking the Kurds, backed by the West, isn't going to do them any favours. Assad's forces are stretched thin, and hunker down in the safety of Russian bases when not conducting operations. For the near term, I think Assad is wise to pick his battles.
4. Iraq - Very much a real problem, as there are a mountain of legal processes that would be required for a new country to be designated, along with borders, currency, government, etc etc. And the Iraqi government, which legally controls the territory the Kurds want, absolutely will not be open to it.
Tricky situation. We support Iraq. We also support the Kurds. Tricky situation for politicians, diplomats, UN bureaucrats, etc.
I would agree, the Kurds probably are screwed. But make no mistake about it, Iraq doesn't want Turkish military forces deployed on it's soil any more than the Kurds do. So it could ultimately make the Iraqi/Kurdish relationship TRUE frienemies in regards to Turkey.