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TBC: fats really do have higher energy density than lithium ion batteries. But that energy does have to be converted into a form the laptop can use, and so there will be some loss, maybe very substantial.
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Yeah! Natural gas based power plants are about 50% energy efficient (source: https://en.wikipedia.org/wiki/Combined_cycle_power_plant#Difference_between_HHV_and_LHV …). But for a laptop, if we used oil to power it, we'd need an internal combustion engine which would make the laptop much heavier...
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Why does it need to be very heavy? Why not try to invent a very small, very light approach? (Not entirely wild about this idea, for climate reasons. But it's fun to think about a bit.)
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