More importantly, a CoC is a commitment by the moderation team to follow a certain standard, instead of giving it a position of "whatever we say is right, if we don't act, sucks to be you". (And at the same time, it's just that, a commitment, it can still be ignored or misused, it's not an automatic fix for anything)

A CoC is an admission that whoever moderates the community is not capable of doing so without having something to hide behind and point at. Culture is not improved by introducing rules-lawyering and avoiding personal responsibility, that is how you ruin it.

Edit: What good does a commitment do anyway, if it guarantees nothing and changes nothing? It's just someone shouting, hoping someone else hears and approves. If anything, that underlines my point about the fundamental immaturity of the decision to introduce a CoC.

Edit2: I understood your point to be that introducing a CoC means a commitment, which is somehow something that is good. When all this commitment does is deflect responsibility, that is not a healthy result. I feel like that addresses your point fine.

A CoC doesn't automatically deflect responsibility. As a moderator you still need to actually moderate, and you get the feedback for doing so. As a commitment, it actually puts an extra burden on the moderator, since there's now an explicit thing people can point to when criticizing your (in-)actions.

I happen to have gained a moderator role in a community that has a pre-existing CoC. I'm not sure why I would "hide behind" or "point at" the CoC when acting in that role, I'm perfectly fine with telling people off (or more if necessary) without doing so.

And yes, if you assume the worst of everybody commitments don't have any value. But people generally attempt to actually uphold things they commit to, and thus it is seen as a positive signal, even if it's not a guarantee. (Ideally we wouldn't need CoCs because the baseline established by them would be such a universal commitment in society that you could just assume it to be valid everywhere, but experience shows that's apparently not the case) Several community members told me that it has been relevant to their decision to interact/join.

EDIT: and even if you say just a commitment is worth anything (as said above, I personally also don't think "has a CoC" is that much of a signal without seeing how mods actually act, but clearly other people do), that's quite a difference from a blanket "CoCs are always toxic".