But we can see how supplementation affects outcomes, and it turns out that so far the results on that are pretty 'meh', unless you're supplementing specifically for severe vit D deficiency.
However, many of these methods try to obtain the conditions similar to the gold standard: Randomized Control Trials.
In an RCT, if you assign treatment randomly to balanced subgroups of a population you care about (or one that is even representative), then you do not require to controls.
To see that, imagine the treatment being independent of the confounding factors and the distributions across group being the same. It then follows that you can estimate the average treatment effect without bias.