To add some context which may be obvious: this scene is global with lots of events and travel. We see each other all of the time, and there is a lot of workplace and personal interaction blending. What starts in online forums or in person at a party ends up affecting our job, etc.
So, basically, with a CoC adopted by the core devs, the problems addressed are those that traditional legal systems cannot address for people involved in the coordination of the protocol and those in the wider community that they interact with.
I think that one problem addressed by a CoC (and some kind of adjudication process) is that of misrepresentation. Often there is a situation in which someone accuses someone else (or their organization), of some kind of misdeed. It would be helpful to have a procedure in which one could say: you have violated this clause of this policy. Then evidence comes out, and it is settled.
Another recurring problem is intimidation, as in the case of Afri (no longer participating in the Ethereum community). Due to some actions he took, community members began ganging up on him in reddit and Twitter, spreading conspiracy theories, and worse. He experienced a great deal of personal stress and ended up leaving the Ethereum core devs, which was a very significant loss to the community.
This kind of situation is probably most clearly addressed in the proposed CoC.
Trolling, insulting or derogatory comments, and personal or political attacks
Perhaps a few people could have had a formal reprimand or certain privileges curtailed due to CoC violations, creating the impression that there are consequences for violations, reducing the tendency to attack.
Perhaps the online attacks against Afri could have been prevented had there been a CoC in place and an avenue to point out his own violations (not that there were any). Those attacking him may have felt that he was harming the community. The presence of a CoC and process alleviates some of the need to attack, because we have agreed that this is the process for finding justice.
Another situation is that of sexual harassment. There are some cases of this in the community. This is covered to an extent by CoCs used at events, but what about outside the context of our gatherings. We are an international scene and sexual harassment and other harms can occur which would basically be impossible to raise objections to, find justice for, except by public accusation. This has its own problems as it can devolve into injustices such as exile without due process.
In the proposed CoC, sexual harassment is partly covered by the following clause:
The use of sexualized language or imagery, and sexual attention or advances of any kind