[AnthonyMouse]

If you want the process to be sustainable then it has to be reversible. Burning 1000W worth of fuel only to spend >1000W of electricity to remove it from the atmosphere and turn it back into fuel is clearly a net cost compared to just using 1000W of electricity to cook your food. Or less than that with non-inductive methods, since electric heat pumps can produce more than 1000W of heat from 1000W of electricity by removing some of it from the environment.

A non-sustainable process that converts fuel to CO2 and then into a solid or liquid that isn't fuel could theoretically have positive efficiency, but it is by no means guaranteed to (especially when the competition is heat pumps), even if it did by a small margin it could still cost significantly more, and it implies that you're eventually going to both run out of fuel and convert it all into an enormous amount of industrial waste.