Catching up on this a few weeks late, I realize, but an important addition to this...
...Which can happen to you in Joinmarket as well. You can get censored by the coordinator and you can't even detect they are doing this.
No, you can't. Makers can choose not to join your coinjoin, and so you can pick different makers instantly. They absolutely cannot ban you from coinjoining altogether like Wasabi can do. (I know you are going to repeat your nonsense soundbite about "run your own coordinator" here, but as I explained above, that simply is not an option for 99.9% of users).
I think it's very important to note that it's actually impossible for everyone to run their own coordinator.
Assuming that we want everyone to be able to mix their coins without possibility of censorship, everyone should use their own (and only their own) coordinator, which would result in an anonymity set of 1 (per coordinator).
Basically your whole model depends on people finding a large number of users who are willing to
not run their own coordinator and therefore put themselves at risk of censorship, for
one user to be truly private and uncensorable.
Besides: is entering a custom coordinator URL even a GUI option by now? When this topic started, one of my issues was that it was basically impossible for regular users to switch to a different coordinator even if they wanted to.
If you want to really bank on this point that 'they can change coordinator run their own', you should also let actions follow words and emphasize it in your docs, install guides, set up process and GUI.
Use absolutely no CEX, today or tomorrow.
This is obviously the best option, and it's never been easier. We have the biggest choice of DEXs we've ever had, we have the most volume on DEXs that we've ever had, and we have the most advanced DEX (Bisq) that we've ever had.
And they're only getting better. Bisq 2 is right around the corner, which apparently also includes Lightning functionality.
A very important thing that Bisq is still missing is ⚡ lightning network.
For smaller trades it is vital.
It's coming soon!