If all you care about is keeping your Bitcoin private from the people you spend it with (even if you forfeit control of your money and data) then why don't you use a Bitcoin exchange instead of a mixer?
Because, almost every exchange I've known cooperates with blockchain analysis firms, and try to de-anonymize every activity related to you. But, using a decentralized exchange (like Bisq) to do BTC <-> XMR swap may not be a bad idea.
The tl;dr is that it's a lot less effective and more expensive.