Oh so you mean make wood gas, burn it, presumably to generate energy and use that to convert the CO2 generated and water to methane and oxygen? That would result in less energy than simply burning the wood gas in the first place, as it will take energy to convert the CO2 to methane.
Yes. The issue is that you don't want to store wood gas.
In the vehicles where wood gas was used, it was produced as needed, not stored. The production process wastes about 30% of the energy in the wood.
Yes, wood gas used in the war, instead of petrol to power cars, but not very many people had cars back then.
About 46 000 between 1939 and 1946 in Finland, for a population of about 3.6 million.
I am kind of inclined to argue that people already have too many cars, so that if a sudden shift away from petrol were to occur, it would mostly be a shift away from personal cars, and not so much a shift away from transportation in general. Buses, not Mad Max.
It would make far more sense to go electric instead.
As long as you have a practical, sensible way to store the energy, I have no arguments there.
Liquid fuels are generally easy to manage, which means some losses are acceptable for ease of use.
The waste should be separated into recyclable, biodegradable and non-biodegradable first.
Problem is, sorting garbage is Somebody Elses Problem. Just look at how difficult it is to get people to dispose of batteries and electronics properly, for example.