Thermodynamics doesn't apply to the body in any meaningful way. It sounds like a 19th century idea of how the body might work that people repeat with no understanding.
And, you not only need to get fuel from the food, but also the materials to build the engines, and for making spare parts and consumables. And everything that actually uses the energy. There will be no energy spent on lighting if you can't get the indium needed for making LED lights, and the body only knows how to make LED lights.
Listen to what you're saying. Thermodynamics doesn't apply to the body? So what, I'm a perpetual motion machine?
The mechanisms in the body are not heat engines. The stuff is so tiny that it works basically by reshuffling molecules, so the traditional concept of efficiency doesn't really apply, as the amount of stuff that happens is given by integral math. You get this amount of charges from reshuffling this amount of molecules. The type of stuff that can be done is limited by how hard the stuff sticks together.
Anyway, the core problem of obese bodies is that they can't produce energy. You can't outwill it, the reshuffling just isn't happening, and there is actually no great reason to believe that fat tissue is some kind of fuel tank, rather than a mass of broken cells.
Also, the body can just reshuffle the molecules in an idle mode. You don't need to spend the energy on moving around.
So what you're saying is the laws of thermodynamics that I learned in school don't apply to biological systems?
I'm admittedly in no position to argue deeply about biology, or even physics for that matter, because I studied mechanical engineering. I dealt with physics in an applied manner.
With that said, this story comes to mind:
https://en.wikipedia.org/wiki/Angus_Barbieri
It seems to disagree with your idea that fat is not fuel. And the first law of Thermo seemed to be applying to this man. He had little to no energy input (via food) and a baseline energy expenditure from just existing, so his system burned stored energy via body fat.