It's probably more efficient to centralize storing weeks worth of energy.
The chain of events is "once in a gazillion century storm wipes power to huge region; millions of households are stuck without power, power company can't go out and fix all the broken things for weeks/months, many people have their houses wrecked by frozen pipes / die from running poorly improvised heat systems"
The round trip energy storage with batteries is pretty good but not terribly cheap at scale. The round trip into hydrogen, theoretically, seems pretty good but the actual "nuance" in the equation is basically a bunch of dragons waiting to eat you and everyone who ever loved you. Anyone selling a "power into hydrogen" thing is probably actually selling a "turn natural gas into hydrogen and sell that hydrogen to hippies" thing.
Maybe if you can figure out how to stick a carbon or two or three onto those hydrogens you'd be in business, but it's hard to get those carbons.
Anyhow, this is a hard problem. People have gotten used to hydrocarbons which are basically magic given their stability and energy density.
I contend that the unsexy combination of solar, a bidirectional grid connection, and an emergency diesel generator is more efficient and environmentally friendly than any existing system involving hydrogen or batteries.
Or maybe you stick three hydrogen atoms to one nitrogen atom and have ammonia.
It's pretty obvious that the single most important reason why the vast majority of machines/engines runs on hydro _carbons_ instead of hydro nitrogens, is that hydrocarbons have been humanity's most important energy source for centuries.
So it makes sense, everything is geared towards them.
But for the future, ammonia appears to be a much better choice, because nitrogen is readily available and the only thing that's missing is matured tech that runs on ammonia. Fuel cells, engines, ...
IIRC there are already container ships being built that run on ammonia.
We would need a gigantic store for heating our house, because for 4-5 months a year, we are generating less electricity than we need. Something on the order of 15MW of storage.
We could certainly our home's thermal efficiency, though this would be complex. We could also add more panels, but then we'd be overproducing by even more during the summer.
For context, I live in the cloudy-ish south of Australia, and have similar problems with our solar power in winter. However, we still produce reasonable amounts of power through the day, and our total winter shortfall is only about 500 kwh, once offset against the daily production.
So for us, 500kwh -> 2080.8 MJ -> 462.4 litres of storage required (assuming 4.5 MJ / litre and ignoring round trip losses), which seems an entirely reasonable for local storage, safety aspects not withstanding.