Exercise alone almost never reduces body fat percentage long term. Calorie restriction of some sort and getting the body to burn fat via fasting/keto is required for most people.

Exercise definitely does improve tons of factors, even if it is not an effective way to lose weight on its own. There is also, as I understand it, some degree of distinction between weight loss and weight gain prevention: while the saying "you can't outrun a bad diet" seems to hold true for people actively trying to lose weight (something I can personally understand, when I'm in a running training block my appetite is unreal), there's also a lot of evidence showing lower rates of obesity in more densely-populated areas, where people naturally walk more, and evidence of improvement when people move from low density to high density areas, which suggests there's a component of just moving around in daily life that can be a factor:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9378543/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6747269/ https://onlinelibrary.wiley.com/doi/10.1002/oby.23634 https://academic.oup.com/edrv/article/43/6/966/6532493?login...

Just do both and get the benefits of thinning out _and_ mental boosts from exercise.

Your body will burn fat in caloric deficit. No keto required.

Fit and fat is much better than unfit and unfat.