btw you could just make the server private key (hardened derivation) the secret for the LN invoice.

Not needing revealing the preimage is one theoretical advantage, but a bigger advantage is that the user gets full, unilateral control of the money after only 1 tx. They do not need to sweep it, as possession of the secret and a sighash_none sig from the server lets the user send the money wherever the user wants to. The server, by contrast, is limited: he can only send the money into a traditional submarine swap address, which the user controls too, since the server has to wait 2 weeks to do anything, and the user does not, as the user knows the secret. So the user has full control of the money in the papa swap address in the same sense that a user fully controls their LN balance. Also, in my implementation, the sig that lets the server move the money into a submarine swap address depends on the existence of a utxo that gets consumed when the user next sends or receives money. Once the user does that, the old sig becomes invalid, so the server cannot even move the money into a traditional submarine swap address.