I mean yea, Putin is a cnut but he kept the other cnuts in line. With the boss gone, the struggle for power within a nuclear state could have dire consequences.
I don't think the war mongering mercenary leading a private army has any intention to pull out of Ukraine either, if anything after assuming power he would up the nationalistic rhetoric to gain support, ending the invasion would make him look weak.
The only hope for Ukraine is the coup turns into a protracted civil war draining all resources.