Even small generators provide a lot of power at once, for a small initial price, but are expensive to run continuously. A battery has low operating cost, but one large enough to run a house off of solar power, year round, is extremely expensive. A battery that is large enough to work 99% of the time is much cheaper, and a generator can fill in that 1%, operating only a few hours a year, at a very low cost.
I ended up with a 6.5kW portable tri-fuel generator instead. It cost me $1300 and I spent a little more for a plumber to add a gas stub to connect it to. I did my own electrical work which saved some money, but wouldn’t have been much more for an electrician. It can run my whole house indefinitely (obviously with some maintenance - it’s a small engine), except for the A/C which generally isn’t needed most of the year, and with some manual load shedding we can run the hot water too.
I live in the city and shouldn’t need any of this, but Seattle is poorly run so we have lots of outages from trees hitting things. Often a different transformer on the same block because the city will repair them but not take the time to trim the trees near the lines on the same block. I’ve had to throw some food away the last two outages (both in the last 6 months) so this won’t take long to pay for itself!
There's no technical reason a generator + battery (and solar?) setup couldn't be configured to run off battery till the battery reaches a preconfigured state of charge then call for the generator.
A business that sells solar with battery backup would know the current product range.
I’m only really familiar with industrial kit tupicalled used in data centres.
I have a relatively small battery as these things go (Bluetti AC200 Max w/ extended battery) but it's enough for our essentials. The game changing aspect of it, IMO, is that acts as a buffer for my generator, solar panels and whatever else I may want to use to power it in the future (maybe an EV?).
The buffer thing you mentioned is key... our average usage is around 400 W, so the generator can be pretty small and the battery system will handle the peaks. We have a hand carryable 2 KW inverter generator. The challenge with this system is that you need 240 V to charge the two Bluetti units (or two 120 V lines on opposite legs of a 240 V feed to ensure the proper phase relationship). I got around this by buying three Mean Well 48 VDC power supplies (meant for large LED installations). Each will do ~500 W. I plug them into the Bluetti units as if they were solar panels. Running the generator through them for 6-8 hours a day is enough to keep the batteries going indefinitely. That's 2-3 gallons of gas per day. And the first day of an outage requires no gas.
In the summer, we have a handful of solar panels I put up in the yard to keep the batteries topped up when not being used for outages (our outages are mostly wind+snow events in winter). Our evaporative cooler, chest freezer, and washer / dryer run off the batteries while the panels are up.