My understanding was always that in the British/French re-territorialising plan post-WW1, Kurdistan was supposed to be created. However, Ataturk invaded the area, and Britain decided it wasn't worth fighting Turkish forces yet again, just to ensure the existence of Kurdistan.
However, recently I read a news article by a British reporter in Kurdish Syria who blamed Kurdistan's non-existence on "America's refusal to live up to its League of Nations responsibilities". I wondered if someone could give some context to this.
While waiting for a response to this specific post-WWI questions, you may be interested in some of my older responses: