That is unfortunately a fairly weak form of anonymity. With a fully public network you can trace even the most meticulously tumbled and laundered tokens. And while they may not exclusively trace back to you, they'll trace into a mixer and out of a mixer with a large majority of the inputs and outputs being tainted.

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.