There have been a lot of studies done on vitamin D supplements, and there is essentially no significant evidence that supplementation is useful for anything. The sole exception is rickets, which is caused by vitamin D deficiency.

https://en.wikipedia.org/wiki/Vitamin_D#Use_of_supplements

There is also considerable debate over the comparative efficiency & effects of natural synthesis via sunlight vs ingesting supplements, compounded by the difficulty of accounting for things like exercising outdoors vs being sedentary indoors.