I think you are trying to simplify something that is amazingly complicated. Metabolism isn’t "just" the thyroid. There’s a whole lot more to it than just thyroid. Thyroid may play a role in the "at rest" part of the metabolism equation. But exercise boosts the number of calories we use. Someone who sits at a computer all day uses considerably fewer calories than someone who has a job that involves intense manual labor. Exercise strengthens muscle. The presence of strong muscle raises our metabolism allowing us to eat more without gaining weight — or even to lose weight — because muscle burns more calories than other body tissues. And that’s just for starters.
We need exercise to become healthy and strong again, and then to stay strong. And exercise helps us to keep our weight issues normal.