Robin Hanson at Overcoming Bias has just discovered that even a short football career takes years off your life (compared which, say, soccer, which adds years), and asks:
...why do we regulate other health harms so strictly, yet so eagerly watch this decimation?
It's an interesting psycho-/sociological question, but a much more relevant policy question is: why do we subsidize it? High school and college programs (which actually draw larger audiences than the pros) are essentially subsidized vocational schools for the NFL, and even the nominally private NFL teams are massively subsidized in the form of stadiums. In fact, opposition to stadium subsidies is one of the few policy issues that almost unanimously unites economists.
It's an interesting thought experiment: without the enormous from public schools and city governments, what would the sports industry look like? Would football still be the most popular sport?