I would like to see the theory tested out in a lab.
Certainly the molecular density of the liquid will be vastly greater than a gas, but I wonder if the energy absorbed by the state change doesn’t offset that.
I also wonder if compressing the vapor would simply cause it to liquefy again.
If you compress gasoline enough, you would liquify it again.
As for offsetting the heat absorption from changing to a gas state, internal combustion engines are limited by heat removal from the block. Too little heat is not the problem.