You can sort of transfer Bitcoin without an audit trail by giving someone the private keys to an account.

I guess, but there's no proof the sender has deleted their copies of the keys. You would need to immediately transfer the assets to another wallet, and until you did, the sender could rescind the transfer by moving the coins themselves.

Although meeting in person to physically transfer gold requires a similar amount of trust, so ¯\_(ツ)_/¯