Here’s my understanding of the evidence* as someone who studies aging genetics in lab animals, which often overlaps with “let’s see if nutrient X helps lab animals” sorts of studies.
Basically there’s lots of epidemiological evidence that a diet with lots of fruits and veggies is very healthy. This is determined by looking at the health of various groups around the world, correlating dietary factors with health factors, and then controlling for other factors which have an effect on health (income, health care access, etc). Study after study shows that groups of people with lots of fruits and veggies have greatly reduced risk of all sorts of disease. That makes epidemiologists happy, though they’re the first to point out that they show correlation and not causation.
So to prove causation, you have to do some sort of controlled study. The ideal experiment to answer your question would feed different diets to different groups of people and measure health outcomes over time. But that’s too big of an experiment to ever be practical – you’d have to recruit thousands of people, give them several carefully defined diets (lots of fruits+veg vs. vitamin supplements vs. control diet), monitor over the course of decades, and somehow manage to enforce compliance among the study participants.
So instead researchers do smaller and more manageable experiments. They test to see if one particular vitamin supplement helps with one particular health measure over a short period of time. And there’s evidence that certain dietary interventions can reduce particular disease risks. But those effects are relatively small, and don’t entirely account for all of the health benefits seen from epidemiological data.
So experiments show vitamin and fiber supplements effectively prevent dietary deficiencies, but otherwise don’t provide very large health benefits. It’s possible that some super-supplement with hypothetical unknown phytochemicals could provide more benefits, but we don’t know what it is. It’s also likely that part of the benefit of eating fruit and veg is that they simply displace less healthy fats and refined carbohydrates.
*I’ll dig for cites later – I already spent the morning on PubMed and that’s enough for today, thankyouverymuch.