I'm starting to wonder how long it will be until the Kurds realise the West is willing to watch them go extinct because Turkey is just too useful as NATO partner, the moment a Kurd takes action against the West is the moment Erdogan can burn their culture to bits.
It's likely his aim anyway, just stoke it enough and it'll spread.
I think you'll find that some of the Kurds are incredibly well aligned and defended by the US. Turkey would not be allowed to do that, they might try, but they would be stopped in the end.