That's a good idea.

However, I'm not sure that revealing your on-chain address is a real privacy issue, since your on-chain address is not linked to your identity.

Furthermore, If there were a few on-chain p2p transactions in the middle would make it practically untraceable. additionally if there's an LN in the middle it would makes harder.

I think that moving physical stuff in the real world has more to do with privacy issues than Bitcoin.