They have a kind of controlled capitalism where they don’t allow the rich to be too greedy or corrupt.
I think it’s more accurate to say that they don’t allow the rich to be become too powerful, which is very different from allowing them to be overly greedy or corrupt.
For example Jack Ma, he’s no more greedy or corrupt than many other ultra successful Chinese business people and China didn’t care about him until he got too popular and he started speaking negatively about the CCP in public. He was popular, rich, and criticizing the CCP so they took him down.
Ren Zhiqiang is another example. The CCP was fine with him being stupid wealthy and corrupt as hell but then he started getting popular by criticizing the CCP and that they wouldn’t tolerate and sent “Big Cannon Ren” to prison as quickly as possible.
You don’t even have to Oligarch status to draw their ire. Remember Peng Shuai? She was popular and became a threat to the CCP after making sexual assault allegations against a high ranking official. They do it to famous people of all types but only after they start criticizing the CCP. It’s not a co-incidence.
Unless someone’s Greed and / or Corruption becomes a threat to the Government itself the CCP doesn’t give two shits. It’s why the people behind Evergrande, Country Gardens, and Zhongzhi got away with INSANE levels of greed and corruption for so long. The CCP knew it was happening and didn’t care until that Greed and Corruption was threatening to topple the economy and thus the CCP itself.