Any sort of battery system that lets you keep running in an outage is going to be pretty expensive, unfortunately.
But at that point your question isn't "what would be the payback period if I got solar" but "how much is it worth to me to have power when the grid is down". And so not surprisingly many people get solar but don't install a battery.
(Systems that provide a small amount of best-effort when-the-sun-is-shining emergency power when the grid is down seem like they should be a sweet spot here, because they can be implemented very efficiently. Unfortunately a combination of consumers not wanting it, the NEC not prioritizing it, and the shift to microinverters means that instead of adding ~$200 like it did when I got solar several years ago it's now more like $7k)
