That's my whole point; that CoCs might be a necessary step for social changes that quite many people don't understand and/or master yet (e.g. custom pronouns) is understandable. But apologize after you hurt someone is something I (and, I assume, most people) was taught when I was 4 y.o. and should be widely applied. What will be next, a little panel reminding you to say "hello" and "goodbye" when you come in and leave, or "don't forget to say thank you" next to the cashier?
If that's your experience I feel bad for the toxic environments in which you must be immersed.
Just this week I witnessed one of my co-workers apologize to another, publicly, in front of a number of their fellow colleagues, for behaviour they regretted.
And yes, it was a genuine apology. And no there was nothing to be gained for this individual, personally, by delivering that apology.
I myself have both given and received many apologies in my professional career. If that's rare, it's only because most people, most of the time, don't behave in a way that warrants apologizing later.
It's precisely the kind of fatalism you express, here, that leads to bad behaviour going unaddressed.
Asking for forgiveness, on the other hand, is admitting that what I did was wrong. That's not necessarily the same thing that I'm sorry about -- as an example, "I'm sorry that ball hit you on the head, please would you forgive me for not being careful enough?". This separates my actions from their consequences in a way that acknowledges their affect on other people.
And I'm quite glad that in most situations I find myself, someone being willing to admit when they are wrong is considered a positive. It builds trust, and shouldn't result in losing face.
That sounds awfully weird for me coming from an environment where accepting your errors and apologizing is seen as the only honorable option; "noblesse oblige" and catholicism-impregnated traditions I assume.
What a CoC does is give clear expectations for everyone in the community. It makes the discussion easier because it's a simple “Don't do this, rule #3” rather than having to lawyer about whether something is a problem after things have already become heated. This doesn't solve everything, of course, but setting a baseline cuts out a lot of tedious lower-level stuff and helps set a climate which discourages bad behaviour by removing the lower level stuff which can encourage it. That guy who infamously used a porn image in a conference slide probably didn't just wake up one morning and decide to do that but was in a subgroup where sexualized comments & humor was normalized.