Why does this feel like Iraq all over again? You oust Putin but what of the power vacuum that is left behind? I can't help but this is a common gambit of dictators: You think I'm bad? Wait until you see what comes after me. With nukes.
There was a terrible civil war that killed far more people than the actual invasion, supported by a lot of outsiders and targeted at civilians. But as shaky as it was, the government remained.
Russia wouldn't have the dubious benefit of American nation-building, but honestly is probably better off without it. The fact that there are nukes on the line is awful, but in the end the next dictator would face the same mutually-assured-destruction math that Putin does.
A scarier scenario is Afghanistan, where the government we set up failed the instant we left. It was replaced by the same guys we kicked out in the first place, and is now fighting its own terrorist insurgency (who are also our enemies, for that matter). If there were nuclear weapons in Afghanistan they would almost certainly have been used already -- against each other.
Russia is, hopefully, a bit more like Iraq. They have the outline of a functional government. It may or may not fall to a dictator; that would depend on the circumstances of Putin's downfall. But the biggest thing to fear there is a failed nuclear state, even more than the specifics of who runs it.
If someone believes parent is wrong, it would be interesting to read why their interpretation is so different.