If all parties use HD wallets, you can use HDM. Then you don't have to remember the public keys that were used because you can regenerate them.
In theory yes, but when multiple parties are involved you're at least going to need to store _something_ related to the other party, even if you've removed the need to store many things.
Deterministic wallets are actually making this problem more pressing, because if you already have to store and back up a bunch of random private keys then you presumably already have a process for storing and backing up new data, but nowadays people reasonably expect not to lose funds unless they lose their seed.
) and people seemed fine with the extra storage needed. With multi sig boxes, the premise of not losing data because you have your seed no longer holds. After all, other people must not lose their seed either. I guess that you are now also required to store the master pub keys of all parties involved which are simply more seeds.