That hypothesis does not fit observation.
Fuel efficiency has gone up since we stopped using carburetors.
Natural gas engines are not 3-5x more efficient than gasoline engines.
If you compress gas, then add heat by burning fuel in it, and expand it back to atmospheric pressure (allowing the gas to do work) then by the time you are back to atmospheric pressure, the gas still has excess heat in it. You cannot convert the energy in this heat to useful work, if a piston is all you have to work with. (if you pardon the pun)
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2016: 128.75L for 1875.00km => 6.87L/100km (34.3MPG US)
2017: 209.14L for 4244.00km => 4.93L/100km (47.7MPG US)
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