Every system will have corruption so the only one that will actually work is one that is at least somewhat resistant to it

The problem goes a bit deeper than just competence vs incompetence of the planner. The planner is a person. A person looks at the mathematical recommendation - and sees that it is cruel: a project should be closed, a lot of people should be laid off. In capitalism, no cruel decision is yours completely: “market forced me to do it”. Brezhnev time Soviet leaders were probably less cruel than an ordinary American capitalist. So the effective economy was out of question.

Also, to be cruel is not enough. You should have a political power to implement an effective solution. Political power is based on relationships. Suppose mathematics says: person A’s project should be reduced, person B’s project should be funded more. But: person A is your guy, and person B is of your rival’s camp. Will you follow the math? It’s probably a theorem: in a planned economy a recommendation that reduces the political power of a person that has the political power to implement it - will never be implemented…