I'd refine it as 'If feasible, try fixing your diet before going for pills'. The body is adapted to function within a healthy nutritional range. If your diet falls outside that range, it's expected that your body won't function properly. If problems persist despite a good diet, then pills become a more reasonable option.

Because it's unlikely that a specific deficiency is your only single problem.

Based on what? You seem to be assuming that the only way to be deficient in something is to have a junk diet. It is quite easy to be deficient in just one nutrient.