the biggest privacy and efficiency benefits of ecash come when you transact fully within the ecash system. you lose privacy and pay fees when you go to another layer, whether it's lightning or on-chain or something else

how does it work in practice?

mints will hold balances of other mint's ecash and settle up with each other at regular intervals via lightning. this is exactly how free banks operated in the 1800s before the state shut them all down

user wallets can do the same thing. when one ecash user wants to pay another their wallets will collaborate in a privacy preserving way to find a common mint they both trust. if no common mint is found, then fall back to lightning and pay the lightning fee

seriously, every bitcoiner should read up on free banking. these are not new problems. they've already been solved. we just need to rebuild those solutions in a new technical medium