Mixers are designed to facilitate money laundering. You can claim it’s for legitimate privacy, etc but it doesn’t change the fact that it’s money laundering.
For E2EE,you describe the base level capability: Secure message between two parties.
For Mixers, you describe an act that the capability of making money hard to trace enables: Money laundering. If you applied a similar argument to E2EE (as many have and will keep doing), encrypted communications are a way for people to do illegal things away from the eyes of the law. Trade illegal items, send banned/illegal/questionable content, etc.
From a pure capability standpoint, mixers, like E2EE, are a way to secure XYZ activity (Which happens to be money transfer) from prying eyes.
You're drawing a distinction between illicit and privacy-seeking transaction and I'm saying the act of obscuring the source is all that matters.
A mixer concealing the public address of clean money is not nefarious in any way and should be perfectly legal.