That is correct, but in the far past it was not always so.
Erdo is a Dictator just like the Ottoman empire was run by. They were not Turks.
I am not disputing your idea but the situation has many angles.
Kurds were Turkey’s enemies not only before Erdogan but also before Kurds became US allies.
Based on that fact alone it wasn’t really Turkish-friendly for US to ally with the Kurds.
A lot was told about Turkey setting obstacles for the secord Iraqi operation but once again it has involved Kurds on US side too.