I think you are delusional on that one. Several three letter agencies had to already admit that they are active on P2P exchanges.

With so little liquidity on the exchanges, the default assumption needs to be that the counter party is able to tie your bank details to your person (and since it’s the counter party also the UTXO) and is an adversary (criminal or Fed).

So this point goes to the KYC light exchanges that at least don’t share your data with the government by default.