> When you increase activity, over the course of weeks, the body adjusts and does everything it can to not touch those fat stores.
Your body doesn't adjust endlessly. The technique to continue to shift body composition is called progressive overload, this isn't outdated and is the basis of most athletic training regimens.
Again I want to reiterate that no one is suggesting that diet isn't the foundation of fitness and controlling body composition. I am simply and factually stating that you can use exercise as a lever to achieve a calorie deficit. Arguing otherwise is to argue against thermodynamics, moving your body consumes energy and you body simple cannot achieve perfect efficiency.