" What is the theory, that with the Mullahs gone Iran will abandon nukes?"
A friendly gov't with nukes isn't a problem.
But here's my theory.....When the regime collapses, the people will busy putting their gov't and country and lives back together and nukes won't be at the top of the list. The country's infrastructure has suffered greatly over the past 25 yrs, so there's a lot of work to do and that will take lots of money. They'll put the nukes on the back burner, so to speak.
The US would have to gamble that the new government will be friendly, stable, and not have Islamic wild cards. The number of 70% against the Mullahs bodes well for regime change. The 30% Islamist does not bode well for nukes in "friendly" hands. I think the "friendly" prediction is wildly optimistic, and nukes are not a good subject to view with rose colored glasses.
The polls I have seen show popular support for nukes. There is a window here. Once they have a nuke we will be in the same position as we are with NK. And that is dire.