Agreed, diet is a poor explanation for developed countries. What seems more likely is that the discrimination start earlier, in college or high school where athletic students have an easier time going to the best colleges simply because they are good at a sport (assuming height is correlated to being good at a sport popular in college)
Height is doubtless correlated with athleticism, but it's fairly weakly correlated. Except in basketball, when you see a group of athletes, you'll tend to see a range of heights. A little taller than average? Sure. But not immensely so.
And then, athleticism is doubtless correlated with admission to elite universities, but, again, only weakly so. The top tier and second tier universities like to see some extracurricular activities on your record, but "being good at cross country running" is far from a sure-fire way to get into Harvard. The REALLY good athletes don't go to top-tier academic universities, and don't get corporate jobs -- they're on the pro athlete track.
You might get into Harvard due to being a good football player but not good enough to go pro, even if you were not otherwise academically capable of going to Harvard. But, first, you're now talking about a small percentage of Harvard students. Second, I'd like to see some data before I'd concede that IF you're clearly not elite-university quality academically, BUT you get in on your athletic merits, AND you go into a corporate track job, THEN you end up with an elite career path.
So, long story short: Is there probably some advantage to height through the path you suggest? Yes, probably some measurable advantage. Is it enough to explain the pretty substantial advantage that tall men enjoy according to the literature? I can't see how. It's passing through too many weak correlations.
