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Oil generators have an “artificially” low price because there’s a lot of demand for oil for other things. If the other sources of demand go away, the price may become unfavorable even if gas generators make a lot more sense from a redundancy perspective.
In this application, at this scale, on the timeline of an individual human: It doesn't matter much.

It's just a bit of temporary[1] redundant local infrastructure that is hopefully never used at all, and when it is used it won't be used for very long. The fuel will remain available for as long as any of us reading this are alive.

The price of the fuel may go up (it probably will go up), but it doesn't really matter much at this scale whether it costs $25 per day to run or $100 instead -- the power grid will come back online soon enough.

[1]: It's a backup generator, not an heirloom. In 50 years, people will look at that old thing and laugh at how interesting its archaic nature is. They might tinker with it. They might give up and have Jeb haul it off as scrap. And that's all fine, too.

The future cost would likely be based on chemical synthesis.
Recovered biodiesel (fryer oil) is always gonna be a thing to some degree. Either chemical synthesis or just plain devoting some agricultural output in the future doesn't sound completely insane.
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Power density of dino juice is virtually undefeated
Hate to break it to you but fossil fuels comes from acient plant and microbial material, not dinosaurs. Coal comes from the Carboniferous period from massive land plants that accumulated in oxygen-poor water. Oil and natural gas mainly comes from plankton, algae, and bacteria that settled on the ocean floor and mixed with sediment.

Dinosaurs contributed an infinitesimal fraction of the biomass that is needed for the fossil fuel reserves.