"it's in the Kurds self interest to be part of Iraq"
And how is this actually true?
Different tribal origin; their own oil resources that the Iraq nation wants to appropriate; Different flavour and texture of religion; different goals; different history.
A merger with the rest of the purely theoretical country of Iraq (read about the late 19th and 20th century history of the region) has limited advantages and obvious dangers to the Kurds.
Th only reason the Kurds play ball is that if they did not, they would be surrounded by hostile countries, each of whom has a grudge against the Kurds. A landlocked and distinctive group has serious problems if they won't knuckle-down to their neighbours' expectations...