Maybe not.
There is reason to believe Prigozhin has become the most popular political figure in Russia in recent months.
If Prigozhin succeeds in forcing Putin to remove Shoigu and Gerasimov without major bloodshed Prigozhin likely becomes even more popular among the Russian people.
Putin and his circle may decide the best course is to reach an accommodation with Prigozhin and sacrifice Shoigu and Gerasimov.
Recall Prigozhin's most recent videos in which he asserted that the invasion of Ukraine was a mistake, that it was done so that certain oligarchs could plunder Ukraine and that Russian losses are much greater than the Russian people have been told.
Always better to have someone else do the dirty work.
Wonder if any Wagners are on board those commercial flights headed for Moscow right now.