Yes, Methanol contains less BTU's per gallon, but the engine burns more.
Gasoline burns at a Air-Fuel ratio of 12:1, that is, 12 parts, by weight of air to one part of gasoline.
Ethanol ("grain alcohol") burns at 9:1.
Methanol ("wood alchohol") burns at 6:1. FYI- most methanol these days is made by a catalytic process from natural gas.
So, the Methanol burning engine will take 2x as much fuel, so half the milage.
"Gasohol" is only a small percentage of ethanol, so that could be run without resetting the throttle body/computer, rejetting the caruretor, injectors, etc.
But to go to straight ethanol or methanol will take a lot more mods, especiall with today's computer controlled engines... oxygen sensors, temperature, the works. It would all have to be worked out and calibrated for the new fuel. If you just dumped in ethanol or methanol in the tank the engine would not well, or at all. It would be far too lean.
Now, Nitromethane... this is neat stuff. It burns at 1.5:1. You really pour that into your "fuel" dragster. If you get the compression ratio on the high side it will even run without air... as a "monopropellant". Which is what gunpowder and explosives do, supplying their own oxygen.
But back to alky... the real benefit of alky is that it increases the oxygen content of the gasoline-ethanol mix and helps engines produce less pollutants. Or so they say.
What it mainly does is give corn farmers a subsidy.