1) Well, that's what he wanted now, to be in charge, or maybe not with Putin In charge. I mean, contract is one thing, you had to have people to complete contracts. And tell me what you think if you are Prigozhin and MOD issue an order having all Wagner sign a contract with Russia MOD?
2) What's Putin was doing is bad for Prigozhin business. He could have gotten contract from whoever in charge next (it may well be him if this coup turns out great) but for him, his people is more important asset than any contract, I mean, now, even if he have contract, who do he send to complete those?
3) On the other hand, you don't use merc to fight a war, you use them on and off, I know a lot of Blackwater (Xe now/) KBR and G4S guy, you don't hire them full time like how Russia did with these Wagner dude, you hire them in term, and pay a fixed fee, I was approached by KBR to do intel work for them in high risk zone, they are paying me $500,000 per contract, and that is 3 months on 3 months off with a vacation of my choice, sure, you won't pay $500,000 for driver or security guard but they also don't work 12 months on, and these merc have been deployed 15 months straight, say if you pay them the rate Blackwater pay their driver, you pay 15,000 a month, 15 months, that's 225k per head, instead of 40k you are paying those blackwater guy, and you are talking about 50,000+ Wagner soldier, you do the maths.
I am not saying it had no other issue than money, but money is pretty big one. I can't see how otherwise it would went over the threshold.
4) Unless they can have a peaceful transition, which is highly unlikely, Russia would need to redeploy stuff DURING UKRIANIAN COUNTER OFFENSIVE. Which is not going to be optimal.
5) The war in Ukraine is finished for Russia, even with a peaceful transition, they won't trust anyone now other than people they can control, and the people they can directly control is shit. That's problem 1. Problem 2 is if they take out Wagner, they would lose a sizable chunk of combat power in Ukraine, even if these Wagner folks is not going to do anything in Russia. They aren't going back to Ukraine, which mean you will expect a sizeable push from the Ukrainian in the coming weeks once all these are done. And that would deal a killer blow to the Russian. And finally, you have other fringe group fighting in Ukraine. If they can do it to Putin Chef, they can do it to anyone, Kadyrov or anyone, they aren't going to support Russia from now on, even if they do, Kremlin would probably will have suspicious on them.