First off, we have the layers of oligopolization, like you've said: carefully marketed and individuated products for sports, film, and music ensure that there's a substantial profit margin there. It's not that there aren't indie films or small sports teams; it's that these companies have convinced people that this is their team and that their identity is mixed in with it, just the way that my girlfriend drinks Diet Coke and not pop.
Teaching is simultaneously much more cutthroat, with tons of schools that are constantly shifting composition and competing for the same slice of some dearth of public funds which first gets siphoned off by the occasionally-corrupt bureaucrats at the top, superintendents and such, who don't have nearly the accountability that the teachers do. Then there is a competition among the teachers, ameliorated somewhat by unions, but there is also a competition between the unions too. All of this ensures that there's money to spare for the pop cultures that's not there for the educational infrastructure. UNTIL... you get to colleges, where there are some colleges which have distinct identities; I still name-drop my undergraduate work at Cornell rather than my Master's at the TU Delft, even though the latter is a much greater achievement. There's a bit more pie around for the professors, and they enjoy much more cushy arrangements like tenure.
If you average over athletes in general, athletes get paid crap. Most of them are teenagers playing in exchange for being taken out for pizza afterwards; then there are adult amateurs and college-level play... You take the typical inner-city basketball player and evaluate his chances of making it to stardom, you're going to be talking about winning the lottery. Even if he has big dreams. Same with actors. But what you're actually seeing in these celebrities is a carefully-played oligopoly causing a great demand for a scarce product, and the scarcity drives these commitments to finding the best-of-the-best that allows stars to leverage that monopoly that all of us have in a free society, our monopoly on our own labor.