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.