CCP leaders are largely technocrats unlike in the US. There are many engineers and doctors in the upper ranks.
Many of us have personal experience watching good engineers become bad managers.
Politics is harder than it looks.
In theory an engineering background should help make better politicians. In practice it isn't the slamdunk you imply.
Well, Xi Jinping and his lackeys are known for their poor educational background, maybe not quite well known in the West.
https://www.youtube.com/watch?v=YSYQpaAI90A