I think projects underestimate how off-putting Code of
Conducts are. I won't touch projects with a CoC, and when
a project that I'm actively contributing to introduces a
CoC, I stop contributing.

These days I try not to contribute to any project that doesn't have a CoC. The project I help maintain does, as do the communities I moderate. If someone can't create a PR without saying things that are racist, misogynist, etc. then frankly I don't want them in my community. If someone is going to be put off by the fact that mightn't be able to say something hateful if they decided they wanted to, then I'd rather not have that person in my community.

Giving people who are obsessed with political correctness
a leg to stand on can be damaging to a community, and
trying to placating such people via a CoC is a lost cause.

I think that's a very negative way of looking at a CoC. Where you see "people who are obsessed with political correctness", I see "people who are tired of being constantly shit on by the vocal jerks in online communities". It's not placating, it's simply valuing people's right to contribute and participate peacefully over other people's right to be jackasses. Sure, you can do that without a CoC, but the CoC is a good signal to people that the people who are moderating the community are on their side.

On the flip side, I've never seen harassment tolerated
even without a CoC. I don't think CoC deter such people
anyway. So IMO there is simply no upside.

I disagree with the assertion that CoCs don't deter people in a community; I have seen first-hand where having a code of conduct was a way of resolving something that was quickly getting out hand and was likely to have ended up with some great contributors leaving the project because they were being harassed by others. I wasn't going to convince the harassers that they were wrong about what they were saying, and I certainly wasn't going to convince the people being harassed that they should stick around in a community that was being hostile. Most people were either unaware of the threat, or else not directly affected and stayed quiet. The CoC was something of a final arbiter to put a stop to the harassment, and I had tried diligently to do so before putting on my admin hat or pulling out the CoC. I've seen many other situations where similar things have played out. Without CoCs people would have either been banned from the project, or others would have left, being able to put a stop to something has helped.

Besides, any kind of potential drama is a no-go, I use my
Github account for work. If I was younger, I'd probably
start over again with a fresh github account that didn't
have my real name attached to it. But not contributing
seems like an easier solution.

If you're neither a maintainer or community moderator, nor violating the CoC, then I don't see where the drama would come in. I have my real name attached to my github account, to the meetups I run, and the slack communities I moderate. I deal with CoC violations at times, and certainly my own harassment, but I'm not worried about "drama" effecting my reputation because I stand by my own behaviors and by my belief in the value of not letting people harass others and crate hostile toxic environments.