There are too many variables in diet. If they study steak every meal vs rice and beans every meal they can come up with one. However most people are not that one-tracked either way. Sometimes the rich eat rice and beans, sometimes even poor manage to afford steak. For steak, did I mean beef, lamb, goat, pork... - this might or might not matter. There is also chicken, turkey, snake, deer, elk - and dozens more animals people eat which might or might not be healthy. OF each of the above there are different cuts (does it matter?), different fat levels (does it matter?). And that is just meat, how many varieties of beans are there, what about rice? What about all the other things people eat?

the effect size will not be high

Yes, the most common example would be clinical trials for drugs and other medical treatments- often have thousands of patients (with recruitment being the limiting factor). There are tons of ways that studies can go wrong, for example when patients don't take the treatment and lie (this is common) or have other lifestyle factors that influence the results, which can't be easily smoothed out with slightly larger N.

I don't know how to fix the nutritionist studies- I'm still pretty skeptical that you could ever control enough variables to make any sort of conclusion around things with tiny effect sizes. This isn't like nutritional diseases we've seen in the past, for example if you look at a disease like pellagra (not getting enough niacin), literally tens of thousands of people died over a few years (beri beri, rickets, scurvy are three other examples; these discoveries were tightly coupled to the discovery of essential nutrients, now called vitamins).