Excellent thread, Thinlómien!
To me, Tolkien associates leadership, generally, with height. Many of the leaders are tall. This makes some sense, as you can see them on the battlefield, and so get directions thus. Also, to further increase the height of the leaders, aren't the helms constructed to add a few inches? Why else the wings and plumes and horsehair things? And just what other purpose do standards serve?
Now, not to get political, but when we elect leaders, do *we* associate height with leadership ability? In local politics, you might actually see a live candidate and so are able to judge his/her respective height. TV changes this, as one is not sure how tall the candidate is, and only during debates can one see the relative size of the candidates. What, I guess, is surprising is that in Middle Earth, heighty is mighty, but in our world - around the world - that's not always the case. Was Tolkien stating a personal, cultural or species ideal? This
local mayor, note, is more of the Tolkien ideal.
Methinks that the instinct is to defer to the larger person. Not only, generally speaking, will this person be able to 'mighty' you into comformity, but also might be able to see danger from further away (i.e. wargs in the distance), standing taller than the rest, and so it's in your best interest to select these persons.
Me - I'm not exactly of mormegilian stature, though almost (and, due to the kids, getting shorter by the day

) - and I do find that strangers will pick me out of a crowd for directions, for passing through a queue, for reaching items on high shelves and for other wonderful leadership responsibilities.