Do you honestly think the government would just sit there and let the military do whatever they want? Or that anyone would recognize their legitimacy if they did? Bare minimum, you'd end up with nearly everyone involved declared guilty of treason.
'Ally' is a word with meaning, and 'standing agreement to defend if attacked' also means something.
I don't actually know if that's the standing agreement though, and I suspect that you don't either?
It's similar; and the military didn't do anything then. Though they weren't technically our allies "officially", as far as I aware; we just made a lot of promises to them we didn't keep.
To the best of my knowledge, promises were
not made to the Kurds. It was 'We have a common enemy, we'll help you fight them,' and nothing more.
But again, I don't actually know for sure. This isn't something I've studied in detail; have you?