A man sends his coins to exchange E and receives different coins C after a while. In your opinion, this is a bad practice
Yes, because an exchange isn't designed to offer on-chain privacy.
Well. Let's clarify. A man sends over TOR/VPN his coins to exchange which doesn't require him to go through KYC procedure. Which private details could be revealed in this case?
On the other hand, if a man sends his coins to a dedicated mixer M, and M sends those coins to the same exchange E, getting the same coins C back and then sending them back to the man, you consider it good practice.
MixTum says they're mixing your coins with investors' coins. I'm not sure about the exact procedure they follow, I don't believe they're just randomly selecting an exchange and sending your coins there, under their full name. You can ask them that question in the appropriate thread. I am not obligated to provide an answer, nor am I able to.
Well, correct , exchange operates with investors' coins, but the coins of the same time will be send back to a man from my example. I think you have glossed over the issue you have faced and turned blame on MixTum.