Many houses have solar panels, but in a power outage almost all of them shut down. Especially with serious blackouts like Texas had or like Europe may have this winter, getting even minimal power during an outage is valuable. Designing residential grid-tied rooftop solar so that it only worked when the grid is up was a serious mistake that squandered what could have been a major benefit of putting panels on roofs. Let's fix this!
When the grid goes down it's important that solar panels don't keep sending out power, which could shock utility workers fixing things. Having inverters shut themselves off is the easiest way to ensure that never happens, but it's not the only way: the inverter could disconnect from the grid while providing power just to the house. This would only work when the sun was shining, of course, and only when there was enough sunlight on the panels for what you were trying to run. A large system in a sunny area could be set up to try to power the whole house, while a less productive system might be set up to power a few priority circuits or even just a single outlet.
Making systems work this way by default would have major advantages in a range of disasters. You would immediately have widespread distributed generation, and so many things rely on electricity:
Communications. Really important for people to coordinate. Even just a small amount of power for recharging phones would go a long way.
Medical devices. Many people rely on ventilators, powered wheelchairs, etc, and these generally only have a few hours of battery if the grid goes down.
Refrigeration. Keeping food (and medicine) from spoiling.
Heating. Even gas and oil heat need electricity for blowers, pumps, etc. and generally will not function at all when the power is out.
Cooling. Fans, AC, etc. Combines especially well with solar, since cooling need is highest when available solar is highest.
Pumps, tools, etc. Even more important during disasters.
Looking ahead to likely winter power outages in Europe, and potential outages here if things get worse  it would be far better if these millions of rooftop solar installs were able to operate independently.
You can install systems with batteries, which would be more robust than relying on however much power the sun happens to be producing at the moment, but large batteries are expensive and I'm not aware of anyone selling systems like this with small batteries. What if we used no battery?
Electrically, this is pretty practical. When we got solar I thought about this a lot and we installed an SMA Sunny Boy with a "Secure Power Supply" (SPS) in the basement. It didn't end up costing much more: something like $250.
Unfortunately these aren't allowed anymore for residential rooftop solar. Starting with the 2014 National Electrical Code (NEC) you need to have some form of rapid shutdown to protect firefighters in an emergency, and in the 2017 revision it got much stricter to where the SPS functionality would have to be completely redesigned to qualify. The only option now, as far as I can tell, is the recently released Enphase IQ8 Sunlight Backup. It's very expensive: I got some quotes and it added about $7k (23%).
I think it's likely that this rule change didn't consider the resiliency downsides of prohibiting the current versions of these systems, and it would have been better to make the change over a longer period with more notice to manufacturers. For example, it took until December 2021 for the first NEC 2017 compliant backup system, the IQ-8 to come out, 5 years from code publication. One way to get most of the benefits of the code change without this particular harm would have been to offer a temporary exception for island-capable solar.
My understanding is that the basic electronics to support best-effort power are not actually expensive, however, and almost all of what makes it costly is low volume. You could fix the volume problem and scale up the benefits by requiring this functionality as a condition for receiving residential solar subsidies: resiliency is something the government has a strong interest in, and that people are unlikely to fully account for since they think the government has it covered. It's too late to go back and require this from the beginning, but what if we announced that starting in 2026 residential solar would only be subsidy-eligible if it supported best-effort power during blackouts?
 I recently bought a generator, just in case. It's a dual fuel one (gasoline or propane) because it's helpful to be able to use multiple options and propane doesn't require gasoline's level of cleanup from intermittent use.