Mixers are risky, trust based and to a large extent negate the whole point of bitcoin's existence.
We both agree on that part, but I don't think that's the big problem. Rather, the big problem comes from the notion that some coins are "tainted", which I observe that you're buying.
It's part of bitcoin's functionality however that transactions are public. We knew this since day 1.
It frustrates me when people who misunderstand satoshi, cite him to support their argument. "Publicly announced" doesn't imply that all transactions are public, and no privacy is allowed. It simply means that transactions must be broadcasted on a network of computers, and then each one can try to add it to the ledger by doing the Proof-of-Work. Read again what you've quoted, and particularly the text before the bolded part.
Bitcoin Q&A: Blacklists, Taint, and Wallet FingerprintingAndreas M. Antonopoulos talked about basic steps from centralized platforms to detect tainted coins and understand about it can help you to avoid problems with exchanges and casinos from your deposits. You can do it by yourself and don't have to use mixers for it.
Sorry Andreas, but that's just untrue nonsense. If you want to solve the problem, stop exchanging with people who view you as a criminal. The suggestion of repeatedly transferring coins to yourself is one of the most misguided ideas I've come across.