I don't think that's the premise, though. The idea is that the sanctioned government will, under pressure from the sanctions, change without the need for regular citizens to start some sort of armed uprising. (Though certainly an armed uprising is a possible outcome.)
Maybe the government will do this because the sanctions hurt their people enough to the point where things are too unstable for their liking. Maybe their economy becomes so trashed that the quality of the leaders' lives is impacted too much. Etc.
I don't think anyone in the West genuinely believes that sanctions will lead to citizen uprisings and overthrown governments. At least not after decades where no such successful uprisings have taken place in long-sanctioned countries like Iran.
But it should also be pretty clear that sanctions on countries like Iran aren't causing their governments to choose to change their behavior either. But I think arguably sanctions on Russia since they invaded Ukraine have had a useful effect. While the war hasn't stopped, it's possible that sanctions have slowed down Russia's progress quite a bit.
Not sure what the alternative is, though, aside from just giving up, lifting sanctions, and letting things develop where they may.