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> You can install a solar+battery system because it makes economic sense and pays for itself

Would take longer than 20yr at current power rates in many US locales.

Highly dependent on where you are, what your electricity costs, and what your backfeeding compensation scheme is (eg net metering). In California solar alone is no longer economically viable with NEM 3.0 but solar+batteries to maximize self consumption is still in that sticky ~7 year layback range - and those calculations tend to assume today’s power prices, that are in reality going up quite quickly.
If you have free night charging plan you can recoup quite faster. My system paid off for itself in 3 years - although I designed and set it up myself, so it was about 3x cheaper than through contractors (and yes I'm in US and I pulled permits to do this).
It's nice to do this for more than just the direct economic costs. The generator doesn't have to run 24/7 since the batteries absorb the excess power produced by the generator. This means less fuel wasted as well as less noise produced. I used to have two small generators that I could run (and team, if needed) but adding a battery component meant being able to sleep at night without a combustion engine burning fuel all night long.
Yup, even better if you power a separate battery charger with the generator, but let loads be handled by the battery+inverter. You don’t need to provision the generator for peak loads (which can be quite high), or even worry about high harmonic distortion from a cheap generator screwing with your electronics. It basically turns your system into a fully ‘online’ UPS.

Also, really handy for diesel gens which will ‘wet stack’ if you only run them for short periods or with light loads.

Provision a generator size which you expect to run say 6-10 hours at a time (at say 70-80% rated load) to fully charge your batteries, and a battery bank sized for 3-4 days of load.

Keeps your total gen hours much lower, much more efficient fuel wise (you can set the ideal load using your charger, and it will keep it that way regardless of increasing/decreasing loads), doesn’t require as big a generator if you have things like AC compressors, heat pumps, etc. with high start loads, and gives you a lot of redundancy and flexibility. It even gives you time to fix your gen or find/beg/borrow another if yours breaks, and you won’t need to keep the gen running overnight if you plan appropriately, so your neighbors will like you more.

Best of all worlds. Especially if you have natural gas, or get a tri-fuel generator and keep propane handy. Propane doesn’t go bad like gas or diesel can.

Will you not own your home for more than 20yr?
I think for most people it would be if they can they afford a 20 year advance on electricity costs all at once. That is a lot of money if you have more pressing needs, but if you got that money sitting around then yea of course it is a good investment.
And in some, like ours, it takes 5.