Yes. It's the difference between willpower, and "drive," maybe this is just how I use the words personally, I look at willpower as forcing yourself to do something you don't want to do. If you're driven to move, it might take willpower to stop fidgeting.

I do think there is a place for structured, disciplined exercise, though. Sometimes habit can fill in for more spontaneous drive. If I work out at the same time every day, my body seems to expect to work out at that time every day, this gives me a consistency I might lack when anxiety or depression are cycling up.

Amber of the Ketotic blog has posted that on a zero carb diet, increasing exercise helps her stay in ketosis on a higher protein intake. Exercise vs. 300 grams of carbohydrate a day is one thing. Vs. zero carb, if you're already eating fairly ketogenically, things are so tight that burning through as little as ten grams of carbohydrate a day through exercise could make a big difference to level of ketosis, if you've got some condition where that matters.

One criticism of exercise is that it can increase appetite, so a person doesn't achieve any greater energy deficit. But sometimes it might be better to achieve the same deficit but at a higher food intake, even if there's no difference to fat loss, a bit more food and exercise is liable to make for increased lean mass and increased micronutrient intake.