Ecash is about a million percent more private than custodial lightning. All other use cases are either improved by the privacy properties or fall back to lightning baseline performance.
Examples:
1. "someone can promise a token is yours" no, actually the mint makes a cryptographically verifiable promise that the token is only claimable by the entity holding the correct private key. This is better than custodial lightning because they don't know your identity so they cannot selectively enforce these contracts. It's very possible to build some kind of staking/slashing mechanism or web of trust if you think reputation alone is not sufficient. It seems like this is a core feature of your proposal. It can applied to mints just as easily as custodial LN wallets.
1a. "a promise is all it amounts to until you get online and talk to the mint" no, you need to know the mint's public key beforehand and have some trust in that mint. In this case you can cryptographically verify the promise from a trusted party. If you don't already trust the mint then it reverts to the custodial lightning trust-me-bro model.
2. "Coins aren't fungible across mints" mints are connected via the lightning network so all it takes is a lightning transaction to reissue at another mint. Many wallets let you configure this automatically so you never even accept tokens from an untrusted mint. Personally, I think the endgame is to have mints directly swap each other's tokens but the cashu team has pushed back on this idea. We'll see where we land in time. IMO it's an obvious scaling strategy. I think we'll build it when demand is apparent, maybe as part of a different ecash protocol.
3. "There's also some parts of the process where you might lose the coin altogether?" yeah just like losing your lightning signing keys. Cashu uses deterministic secrets with a 12 word recovery seed phrase so you can recover your coins if you drop your phone in the toilet. This is equivalent to lightning. You should look at the spec, you have knowledge gaps for big important protocol features.
4. "The only way for an operator, even an honest one, to stop is to rug everyone." this is true today. I think we have to build expiring ecash to solve this problem. This is an inherent feature in ehash so I'll probably be the first to build it. Mining shares have a TTL, they are only valuable in a limited time window so if you wait too long they become worthless. Easy to enforce with a TTL on the token. Extend this functionality to bitcoin backed ecash and you end up with the same UX as ark: wallets have to periodically come online to refresh their balance.
I skimmed your proposal. I don't understand it yet but on the surface it seems to be 1. lacking in user privacy and 2. have an optimistic game theoretic security model. Current DOR lightning channels rely on optimistic game theory and the security problems are manifold. They do the best they can to minimize failures but the attack surface is just so large. This is why LN-symmetry is such a huge upgrade. Game theory is a weak foundation to build on IMO.
This proposal seems like a strict downgrade from ecash. You still have to trust someone and the user has zero privacy from the operator. (Correct me if I'm wrong.)

