But why would you do that? You get no benefit by having a mint in that scenario if you are the only one using it. You would be privately shuffling tokens inside the mint to yourself from yourself. I don't know how that helps you.
As soon as it leaves the mint, it is no longer private again, and you remain just as anonymous as before you entered the mint with your KYC-free btc. In other words, the mint was a completely unecessary step.
And if you are sending tokens from your mint to other users, then we are right back to it being custodial for other users.