You certainly can, provided you have a truck, and a DOT certified fuel trailer, and a transfer pump.
That system also allows you to participate in oil futures as an end user, not to mention it lets you keep your generator up and running for a very long time.
Downside is, modern e10 gasoline tends to adsorb water from the air over time, so fuel isn't stable long term. Most guys doing this are running diesel cars/gensets for that reason.
The model is, go to a truck depot with a 300 gallon trailer, fill up trailer and truck, park the trailer at home. Then fuel the truck off the trailer until it needs to be filled again, repeat. Do understand that, you can get a larger tank, but anything over 1000 gallons requires a placard/permit to haul around. That's in a single tank, so, in theory, a legal length 5th wheel trailer could have multiple tanks under that and be compliant. If you want the tanks attached to a vehicle itself, the maximum size is 150 gallons, hence why semi trucks have multiple fuel tanks that are smaller than that.
Really the only difficulty is finding a place nearby that is willing to sell that much fuel to an individual.
Is running a generator for long periods cost effective? If someone lived where the grid wasn't reliable, and could make the initial investment for all this fuel storage stuff, why not do solar?
Usually it's a backup thing, not a 24/7 thing. If you're really out in the sticks, solar/battery/genset is a very likely complete system. I know of a couple places way up north in Saskatchewan that have what amounts to a mining village running off a big portable genset backed up with batteries, and one of them I know was just on a very big genset, and they were able to pay for a battery bank by downsizing their generator significantly due to the disparity between peak load and average load. I'd share the article I read about it, but, in spite of my normally excellent google-fu, I've been unable to find it.
Either way, people forget about this, because if you have any sort of power generation, doesn't matter the method, if you go over capacity, you have brownouts/blackouts/grid failure/etc. What is deployed now, for the most part, is sufficient genset capacity to ramp into peak load, and most of it is under-utilized the majority of the time. Batteries eventually pay for themselves because of this, as they allow for peak load handling in addition to allowing generating capacity to stay online and remain profitable outside of peak load events. It really is revolutionary.
More or less, gridscale batteries are what dams/reservoirs were to water systems, and if you consider the impact of us as a species being able to save water for later use at-will, the promise we're looking at is going to really change the way we live.
Here in Ukraine, the grid is no longer 100% reliable for obvious (and highly intentional) reasons. Solar is somewhat inconvenient to use in large cities, and cloudy days are common. A variety of generator types and sizes can be seen instead. Living in an apartment, I have an Ecoflow Delta 2 Max as my first line and a 3.5kW gasoline/natgas generator as my second line. Most of the time, there is some power at some hours of the day, so the Ecoflow can store it. If it runs out, I can run an extension power cord down from my balcony, lug the generator down into the yard, and use it to charge the Ecoflow. I do have plans to buy a solar panel and put it on the building roof with a Starlink, but it would require negotiating with the neighbors and stuff.
Gasoline storage really is an issue, though. Currently I just hope I'll have enough money to buy it as needed.
"You mean I can't just drive the car? I need to think about how to find fuel for it every couple of days? And then I have to drive there and hope nothing explodes?"
It takes me significantly longer than that. The pumps aren't infinitely fast. The cashier is serving other clients. I have to drive to the gas station and back. All of that adds up to more like 15 minutes.