According to the FAQ I read on chipmixer, they do mix coin and hand over the private key of the coin to the person that want use their mixing service. I think the private key will be generated in a way it will not be manipulated and only you will be able to check and see it. Correct me if I am wrong. Although, there are different ways mixers can mix bitcoin.
Back when Casascius coins were produced, there was a big issue surrounding physical coins:
how and why should we trust a coin mint printing private keys, when the mint generated the keys itself?
If a website gives you a private key to an address that has already been generated and filled with some coins, you can't trust them for "hiding the keys after generating them" or something like that. They owned them before you do, so they may as well still own them if that makes sense. I really do need an input from someone else though: does this count as
non-custodial, as soon as you
also have the privkeys?
I think this is a nice suggestion, but I know about Dash and Zcash too, they are cryptocurrencies that can not be tracked, any wallet that provide decentralized exchange is good enough for this.
The XMR vs DASH vs XZC debate regarding privacy is a big headache and pretty subjective tbh. Dash and Zcash, AFAIK, have
optional privacy. That's a double-edged sword. Theymos has posted
a Reddit reply to someone's thread which is a pretty interesting read - so is
this post about Dash's privacy features. They're quite old though, and things might've significantly changed since then.