I know it doesn't really answer your question fully, but here are some pretty good sites about the history of American football, they might give you a little insight:
History of American Football
Interesting site about Walter Camp-"Father of American Football"
Walter Camp
History of American Football on About.com
American Football
I think a lot of it has to do with tradition--Football started out as a college sport for men and that tradition has held strong for over 100 years. People who attended a college or university have a lot of pride in their Alma Mater. One way they show that support is through their sports teams and for many of those schools, football was one of the first organized sports teams. As the number of alumni from colleges and universities grew and their children and grandchildren became students, the popularity and attendance at football games grew as well. I also think in the recent past (20-30 years) the media has helped that growth tremendously.
Money, of course, is always a big incentive--teams that win have happy alumni, happy alumni give more money to the school. So it always behooves the school to try and have the best teams possible as to get the most wins. Scholarships are a big part of that, as is family loyalty (dad played football here, so the school really recruits super-star son to play football here, too). A winning team also means better ticket sales, higher attendance and more income to the school from games. Which in turn also means better players will want to play for that school and the cycle repeats.
Football is something that is completely American--it may have some of its roots in Rugby and Soccer, but, excepting the EFL and CFL, it is one of the few sports that is played solely in America. In other countries it is known as "American Football" (I know it is because soccer is called football everywhere else but America, but that title just reinforces the fact that it is an American phenomenon.) Many times little boys are groomed from an early age to learn how to play and love the sport--they are given little footballs and jerseys and team insignia from the time they are born. Their dad takes them out and teaches them how to throw and catch when they are about 4-5. They go to college games with their families. They watch it on TV. They play on the pee-wee leagues. They play in jr. high. They play in high school, and many of them want to continue playing at the collegiate level because they have been playing so long and love it that much.