There are inverters that support battery backup, recharging from solar and grid power that are supposed to go between your grid tie-in and the rest of your house. Quite a ways more expensive, but the battery capacity is probably relatively cheap compared to UPS power and is essentially a backup for your entire house.
The one I read about a while ago was a Growatt that is basically an all in one box. Can provide power from batteries, recharge from solar or grid power, feed back excess solar power to the grid, etc, you name it. And I can imagine other brands producing the same solution.
I'm lucky enough to live in a country with almost no power cuts though. I think we have at most 1 a year for max 10 minutes. So can't say I have any experience with it myself.
Charging from the left side isn't all that either, some macbook pro models actually become slower due to thermal throttling because charging from the left creates heat closer to the CPU. Resulting in a significant CPU slowdown.