Earlier quoted context omitted.
The blockchain and every transaction being public effectively disproves your entire supposed usecase.
But wallets aren't associated with a real person by default, unless it's created through some service that does KYC. If you can get anonymous tokens in an anonymous wallet, who cares if the transactions are public?
Most exchanges, etc won't really touch accounts or UTxO that are messing with mixers.
Because of that it's generally just better to use "properly" private and anonymous blockchains instead. If they are fully opaque then tracing becomes effectively impossible.