Does it? Who does it work out well for? Franchises continuously extort tax-payer funds for stadia,some team switches host cities every few years, and the for-profit corporations are legal cartels that decides who gets to own a team. The number of ad-breaks is horrendous to anyone who's watched sports elsewhere.
Internationally the standard is non-profits. Most sports have both their international organisations and highest standard of play organisations as non-profits - football, tennis, golf, cricket. The international components of baseball, american football, and basketball are all non-profits (though they are lower standards of play than the US internal leagues).
Lastly, football is a grassroots participation sport that is seen by its fans as more of a religion than a conventional act of entertainment. Of course, religion in the US is also often for-profit, but hopefully you get the point.