It just dawned on me that CoC docs are basically HR for open source. Point to a violation and voila, that person is gone. “Sorry, nothing personal, CoC violation, there’s nothing I can do”.

Exactly. Without a CoC the persons making hard decisions have to stand behind them. With a CoC they can hide behind the CoC and wash their hands in innocence. This lowers the barrier for making questionable decisions and overall decreases honesty. We've seen this with the suspension of Python core maintainer Tim Peters.