This is futile. The people coming up with stuff like Schnorr signatures and coinjoin are like old-time engineers trying to build perpetual motion machines: undoubtedly very clever in their way, but unaware (or in denial) that what they’re trying just can’t work.
In any cash economy there’s going to be clean money, and money that is dirty to various degrees. Even in hard cash economies where money doesn’t come with a proven chain of custody, it still has a history, and that matters. At the point where authorities start to care, the lack of a CoC becomes YOUR problem instead of the government’s. You can’t easily purchase a yacht in cash, and if you try, expect trouble.
To move money from the dirty side to the clean side is what money laundering is. To do that, you need help from people with clean money. Or at least, cleaner money.
Now you can get that help willingly. In that case, expect to pay a premium. I am told that it’s about 50%. A dirty dollar is worth half a clean one. Or, you can get the help unwittingly, from someone who doesn’t realise what they’re doing. That’s maybe preferable for you, but not for them. It’s probably not sustainable.
In pratice, on the blockchain: You have some dirty money. You want to mix it with clean money to make it undistinuishable somehow. Let’s say you have the perfect solution for this. Call it SchnorrJoinMix 2.0. Great! Only that little problem: who will be supplying the clean coin for the mix? What’s in it for them? Or do you hope to rely on dupes, for free?
For that matter, maybe your coin isn’t the dirtiest coin around. Maybe you sold cannabis, but account 986e28e148efe2ffb500c927277b3a79 over there, he paid for a successful hit on a politician. Are you sure you want to try washing your coins in the same laundry operation as his?
But let’s say you through some magic managed to overcome that, too. You have the perfect payment medium — MaybeDirtyCoin — that can work as a coin without having a chain of custody!
Then you have the problem that various incarnations of HonestCoins, that DO have a chain of custody, will still be around. You have only succeeded in distributing the dirt evenly through coins in your own MaybeDirtyCoin economy. And as with hard cash, the lack of a CoC will quickly become your problem instead of the government’s. The best you can hope for is that it will be allowed to exist to some degree, but trade for less due to its lower utility… say, 50% lower. You’re back where you started.