Do you need cold storage to be sovereign or having the ability and the choice to have your wealth in cold storage is enough under a bitcoin standard?
You need to be able to access cold storage to be sovereign. You can't walk across a border with an LN node backup in your head. No one should ever store their life savings on a hot wallet. We've seen even devs can't gaurentee safety for funds on a hot wallet. Cold storage for savings. This really has nothing to do with layer 2 in my head. It's the hot wallet component, and unfortunately L2 has to be hot as of now.