If those casinos or exchanges are non-KYC then that might be possible but the source is still exposed to them and if harvested can be linked to future transactions.
The only problem I have with your explanation is that you are making the assumption all third party mixers are mixing in a manner that will lead back to the source after blockchain analysis. If any third party mixer implement conjoins as their mixing process, how is that less private than using a third party coordinator (Kruw or Open Coordiantor) for coinjoins?
Did you ever test anything on the lines of this?
Yes, I've addressed this point, if trusting a third party with your financial data is considered acceptable, then using an exchange or casino is superior to a "mixing site" because there is actually an underlying service that provides more liquidity for deposits and withdrawals: