If that happens I will need to spend a full half of a day to collect addresses, check which ones were deleted and then again one by one I will need to sign and broadcast.
You don't need to do anything like that. Just save all your unconfirmed transactions in separate files, and if they get deleted after 2 weeks, re-broadcast them. (Not sure, but I think Electrum will store them in your app data by default if that ever happens, but do the process yourself to be sure)
The feature is available in some wallets like
Muun Wallet which is 2 of 2 multi sig wallet.
What happens if one of the channel partners need to sign a transaction? It could be anything. A regular payment made by them, routing a transaction, issuing a penalty transaction. The multi-sig other end must be present at all times, and it doesn't make much sense. I neither find anything in lightning's documentations.