I think it's a mistake to evaluate sport by only looking at the very highest level. Almost nobody competes there, and in professional sports, I'm not sure that's always where you would find the best role models either :-)
Also, I think you have touched on 3 different things - military training, martial arts training, and sport. (The MAs that we practice today are no longer military, in general - IMO - although they may have that in their heritage somewhere.)
I believe that classing these pursuits as "higher" and "lower" is misleading.
I don't believe any of them necessarily make you a better (or worse) person, although they all have that potential.
s a thought on that point -- worth thinking about in terms of social value beyond mere pleasure, but also I think, in agreement with Mark, those are purposes distinct from the means or purposes of martial arts.