Well the thing is nobody knows you owned ecash outside of the mint. It's Bitcoin in Bitcoin out and Lightning in the case of Cashu.
I guess that is an ever slight difference, but not sure if it is significant. Why else would you be sending to a mint (if that address is known and associated with a mint)? Will at least evoke major suspicion And if you p2p trade or atomic swap for Monero - this is essentially the same thing as sending Bitcoin to a mint. Probably even better. No one will know you got that Monero aside from your peer (and you'll also likely be anonymous or pseudonymous with these methods too)