wouldn't that defeat the privacy purpose? wouldn't someone be able to see that it was your card in the ATM, when they traced back the monero as exchanged for a coin that was exchanged for your fiat?

ETA: just to be clear - that's a genuine question. I don't know much about monero, so if it really is possible to have untraceable money, that seems like a prudent investment for precaution. I've just always assumed that digital money is inherently traceable, so I always assumed genuine privacy is a mirage. I assume I'm wrong about that, somehow, so I'm curious about the mechanisms of that anonymity.