I don't know about China but the U.S does not have term limits for Congress. So. No. It does not have a rotation.
And because of Citizens United, and Israel, "elected officials by the people" might be a subjective interpretation of our current politicians.
Term limits = limit corruption. That's something that's a big problem with our justices as well.
Also , most leftist, who support communism, consider communism to still involve money being exchanged.
I don't think Marx advocated for no money to exist or be exchanged.
We can't do trade and barter for everything.
It sounds like your interpretation of communism is a hippie commune or co-ops. Not really the same thing.
Hippie communes can only work at a small scale. Same for co-ops.