This incident almost looks staged. Its possible Putin and Prigozhin had planned this 'rebellion' beforehand, as a way to clean house.

The Russians bungled the invasion of Ukraine last year. They were supposed to capture Kiev in a fast operation and collapse the Ukrainian government, and then partition it into a rump state. The Generals obviously underestimated the resolve of the Ukrainians and didn't adequately prepare their own forces. The conflict bogged down into positional warfare, and the Russian performance has been mediocre. Their tactics are uninspired, mainly relying on their artillery to pulverise the Ukrainians. Recruitment drives have been disappointing, too.

Prigozhin was sharply criticising the Russian generals for their incompetence, and Putin must have agreed with him (even if he said nothing publicly). As the leader of the Wagner PMC group, he was able to achieve results that eluded the Russian military. Wagner recruited prisoners into their ranks and used them in human wave attacks; these tactics were brutal, but effective. Prigozhin was able to capture the fortress of Bakhmut after months of fighting. His criticisms of the generals carried weight.

Part of the deal that was reached with Prigozhin was reforms to the Russian military, and Wagner PMCs being offered contracts from the military. This was something that Putin must have wanted, but was unable to achieve on his own. If he tried to clear the Russian military of all the dead wood, they would have turned against him, and launched an actual coup (not this staged 'rebellion').