Here in Europe, we have at least 3 exchanges [1] that you can simply make an IBAN money transfer to, and they return you the BTC.

How do they know to what BTC Address to return the coins? They recognize either your bank account number or a number in a text field that you registered with a xpub or a BTC address.

These exchanges do not know their customers, only a set of random bank accounts that transfer money to them.

If any government wanted to know the customers of these 4 exchanges all they needed to do was to pull the deposit information from their bank accounts (assuming on the senders end, there are no anonymous bank accounts).

So, non-kyc exchanges may be a pipe-dream even if they themselves do not ask for and save any information at all.

[1] These are in no particular order: https://getbittr.com/ https://relai.app/ https://pocketbitcoin.com/