Yeah! That has been my idea for a long time! When thought about it, I began looking into devices that can output DC and charge a backup battery but with a variety of input power sources, Solar as main source and line AC as backup. Didn't get that many practical search results.

But it seems what I was looking for are boat chargers. They're meant to provide energy through solar/battery and charge at the same time while parked on a deck. Didn't followed it up though.