So let me know if I understand cashu/Ecash:
A user sends sats via lightning to a mint.
The mint sends Ecash to the user that is 1:1 valued against the sats sent to the mint.
User can now send peer to peer Ecash to anyone with an Ecash wallet.
Or user can redeem sats for Ecash at anytime.
What did I miss?
That's it. Ecash is only transferrable as long as the mint is in operation.
Ecash can't be exchanged through a different mint than where the lightning payment was made to, it needs to be redeemed over lightning to swap mints.
The lightning node attached to the mint could be offline, its channels saturated or unroutable.
The ecash token is essentially a fungible "remote control" over a quantity on the mint's lightning node.
