Worse is that "the Kurds have been fighting each other for 200 years". The reason that there are still Kurds around is that they haven't fought each other, but instead have fought together everybody else that's come along to a standstill, for thousands of years. Persians, Greeks, Romans, Arabs, Turks, the British Empire (which resorted to dropping chemical weapons on them), and still there they are, featuring on the world stage and a force to be reckoned with. The same people Xenophon described two and a half thousand years ago.
I suspect Erdogan's going to regret his campaign, and not just because of anything the US does. Kurds are the definitive enemy that plans do not survive first contact with.