State governments have a lot of people on the payroll. There are legislators, judges, social workers, inspectors, police, and the educational system, from elementary school to state universities. Deadspin looked at the records and determined the highest-paid employee on each state's public payroll.
Based on data drawn from media reports and state salary databases, the ranks of the highest-paid active public employees include 27 football coaches, 13 basketball coaches, one hockey coach, and 10 dorks who aren't even in charge of a team.
Those "10 dorks" are also university employees: chancellors, presidents, or deans (and then there's Nevada). At the link, you'll find more information about where the money for the coaches comes from, and where it might otherwise go. Link -via Digg
The various military services do have sports teams that receive perks above and beyond their salaries.
And for a few it is a career development. Although the rate at which a college sports player ends up going pro is 1-2% (although apparently 10% for baseball), that is not much less than chances in some other fields getting to what the training leads to. Physics graduate school is heavily biased toward teaching academia practices, but a rule of thumb gives about 5-15% actually ending up with a career in academia.
I think the answer is because it's not the place for that, the military is a place where people train and defend our freedom, the police are there to protect and serve the law, and well.. you get the point.. why is college not the place to train and develop people's careers? how do "professional" sports fit in there?