And, to be honest, most of the elite athletes don't make a lasting name for themselves. Willie Mays, yes... Michael Jordan perhaps... but Larry Bird? A great, even dominant player but do the kids of today even know who he is? I've heard of Kareem Abdul Jabar, but I couldn't tell you which team (or teams?) he played for.
The star of 'elite' athletes burns brightly, but fades quickly, whereas literary achievement can be passed on and on and on from generation to generation. The good stuff endures.
I think low production value and Jackass are pretty far off base. You are correct that nobody thought of the bard as highly as Virgil; it is also true, however, that the only way for him to reach that rarified air would have been literally impossible. (Travel time and become an ancient Roman).
Not sure what I'd consider something equivalent in modernity. Maybe something like Lord of the Rings? Hugely popular appeal, enjoyed by a wide range of social classes (something Shakespeare was famous for as well), yet incredibly rich and deep.
I guess I'm just nit picking here, but it is an exaggeration to make too strong of a comparison between a low quality YouTube video and Shakespeare, even looking in the context of their histories.
I think you are grossly overestimating the social position of actors in the days of Shakespeare, from what I've read they were regarded as little better than prostitutes (and some were, they were not at all well paid for their stage work).
Additionally, your 'nitpick' about Shakespeare being compared to Virgil etc actually proves my point, that we tend to hold older writings in higher regard than modern writings. Whereas with athletes, this is not the case. Roger Bannister is famous for running the first (recorded) four minute mile, whereas today running a four minute mile isn't even considered noteworthy. Sporting records regularly tumble, and when they do the athlete that set the previous record diminishes a little in our eyes (I'm not arguing that this is good or right, just that it is), whereas Shakespeare and Tolkein are always going to be up on their pedestals.
When I used to read lots of Fantasy I would pick up books in shops and read the blurbs on the back, and almost everyone was going to be 'the next Tolkein' or 'bigger and better than Tolkein' or some such hyperbole. Now I can easily imagine someone being better than Tolkein (he spends an entire page describing a forest just talking about trees for goodness sake. They're big green and leafy, move on for goodness sake!), but you're not the next Tolkein until everyone compares their books to you instead of him. If you see what I mean.
And of course Shakespeare of Topeka is also competing against the established brand of the original for access to existing theaters and against all those athletes for a slice of the public's leisure time and disposable dollars.
In many ways the Bard had it easy, there's only so much entertainment value in gin and whoring. If he had to go up against American Idol, things might have been quite different.
I do think that the author misses the point when he compares producing a major league player every 10-15 years to be the same as producing a "Shakespeare" every 10-15 years. Producing a "Shakespeare" every 10-15 years is like producing the best of the best every 10-15 years. To play in the Major Leagues, you have to be one of the best, but amongst that elite group, only a select few can achieve "Shakespearean" status.
To produce a Shakespeare, Einstein, or a Michael Jordan requires some luck, and they are characters in history that will be remembered for a while. But it should be possible to cultivate a culture that can foster more talent in the academic fields.
WRT the sports thing: do you think some of that difference could be ascribed to the simple fact that we don't play the same sports as they did back in the day? While sport isn't a modern invention, the particular sports (and the fierceness of pursuit due to the money, fame, etc.) are new.
And finally, I'm not sure if my comment further proves your point, or if it means that we can only compare literature to sport in comparable times. If you accept the idea that sports used to be less important (possible due to the physical nature of regular work and the lack of leisure time), then you can really only compare sports (nearly exclusively happening in the 20th century) to 20th century literature.
In short, sports have just started to catch their stride.
Further, it could be argued that the ethos of the warrior was the true analogue of athletes in premodern times. Hercules, et al.