> You can exercise without changing your diet, but you won't loose (much) weight.

Exercising without changing your diet is seriously nontrivial for most people, due to compensatory eating - if you burn an extra 400 kCal, you will likely experience commensurate increase in appetite & eat an extra 400 kCal. It takes a lot of vigilance & discipline to avoid that.

IMO that's the 'real' reason diet is a more effective lever for weight loss than exercise. In theory, burning those extra 400 kCal thru exercise is just as effective for creating a caloric deficit as reducing daily consumption by 400 kCal, but in practice it still requires you to eat less than what feels normal/adequate.