yes, non-custodial LN privacy is pretty good. custodial is as bad as it gets though. ecash has other properties that make it particularly fit for nostr, such as being able to pay offline (no communication with the mint) and the fact that it's a bearer asset (the data is the money).
Discussion
don’t you need to check with the mint to know its valid? how does offline work.
I guess the faster who remints the tokens wins? Or you lock it pk if offline?
sending is just taking the proofs from your DB and sending it. you probably mean receiving? when receiving you can check the dleq proof to see if the signature is valid. if it isn't locked to your pubkey, you must talk to the mint to prevent double spending.
This is something I was thinking about the other day when you talked about million TPS. Presumably, an end user won't want to lock a bunch of funds to a service provider with no option to reclaim unused ones.
Do you have thoughts on that? I suppose a timelocked alternate spending path would work, but that becomes troublesome if you have a bunch of timelocked tokens on the verge of expiration, too.
with p2pk you can add a timelock to reclaim it if you end up not spending it.
What do/should be done when you have p2pks very near to expiring? It seems like you just end up reverting to the "worst case" of the recipient needing to immediately redeem tokens and/or senders needing to redeem them into new p2pks them before sending, which ends up putting load on the mint.
I suppose if users had the timelocks semi-randomly distributed, then only a subset of tokens would need to be urgently redeemed?
If you run a lightning node non-custodial is pretty good. If you use phoenix or similar LSP type setup the privacy is not very good.