I wope up thinking about this exact idea, this is crazy.
But what I was thinking is that nostr message metadata are public, so having all cashu payments come to your inbox might not be great, privacy wise. 
Is it possible to have 1 nostr npub that generates sub-npubs, like Bitcoin does with addresses?
So the forwarder (cashu.me) would know the main pubkey but each payment coming to a different address.  

 Implement BIP85 nostr keys 

 The bridge generates a new key for each sent token 

 Then the sender is used once.
So the only public information is that a user has an incoming message from a random npub. Not much of an issue suppose.
This is awesome!