> While you're right that exercise can help on the margin, it's just not a useful intervention that moves the needle much as far as weight loss goes.
There's more to exercise than just the thermodynamic effects of calorie expenditure. Building muscle and/or cardiovascular capacity will improve your quality of life and will complement any weight loss. You can improve your mental health by becoming more physically active, and this is well established. Those mental health gains and physical health improvements make it easier to maintain a better diet. Beyond the marginal, but significant calorie expenditures you can create a positive feedback loop.
At one stage, I started walking home from work at my fastest pace. 5 miles, 5 days a week. No other lifestyle changes. No significant weight loss.
A few years later, I started tracking calories with myfitnesspal and keeping to a limit (1600 initially, 1400 when it became easier). No exercise, but steady and impressive weight loss. I seem to have kept most of it off. I think a lot of it becomes psychological - not being afraid to feel appetite or skip meals if already satiated from earlier.