sort of, but not quite...
(just to establish, football will stand for American football)
99.9% of football players in the US play for their high school team. When they graduate, their only realistic option of having a pro career is to first play college football since the NFL has a rule that you can not be drafted until 3 years after your graduating high school class. So, the best players between ages 18-22 are playing college football. Unlike baseball and hockey, there isn't a minor leauge or juniors system for the player to go into nor can you go pro right after high school.
College Football (which is amature) became popular in the 1890s to 1900s. Professional football didn't become popular until the 1950s (the NFL started in the 1920s), part of which was due to the popularity of TV. The college game was the popular version when it started.
Since college football became popular before TV, they needed large stadiums. The Yale bowl (for Yale University) was built in the 1910s and had 70,000 seats. Most large college stadiums are old, have been expanded upon multiple times and tend to have cheaper seats. NFL stadiums, on the other hand, are new and full of luxury boxes since they need to generate money to pay the players.
Colleges and universities of today's biggest and most popular teams (who are also the ones with the largest stadiums) are state sponsored schools, so they appeal to the general population. They have alot of alumni (schools that have existed for 150 to 225 years) and your university isn't going to threaten to move. So there is a lot of loyalty to the school that goes beyond football. The NFL, while it has a large number of fans, teams are newer (10 to 90 years) and can threaten to move. NFL loyalty can be a bit more fickle.
College football is played on Saturday. You can watch games from noon to midnight on 8 or more different channels. You can choose from 20 or so different games each Saturday. There are no blackouts (there is no 3 pm blackout like in the UK). Any team can be on tv. If you have a 100,000 seat stadium and only 80,000 show up, you can still be on tv. The NFL, on the other hand, is played on Sunday. The home stadium has to sell-out by Thursday or the game is blackedout in their home market. So smaller stadiums help ensure sellouts and the game will be on tv. Until the 1970s, the NFL actually blacked out all games in their home market, even if they were sell-outs.
Some of the largest college stadiums are in the south east (which lacks the large cities of the north east and midwest) and didn't have any pro football teams until more recently. So, college football was their only option. Currently there are 124 colleges playing top level football. Of those 124, about 60 of them are seen as the best schools in the top conferences. The NFL has 32 teams and just about all of there are in large cities.
College football needs money to pay their coaches (top coaches earn millions), to upgrade their stadium, practice facilities and travel. Money comes from tickets, tv contracts, alumni donations and student fees. NFL teams pay all of the above and also have to pay multi million dollars in salaries. The money comes from tickets, tv contracts, and corprate sponsors who buy luxury boxes in their stadiums.
Last, you have 300+ million americans with disposable income who could potentially fill football stadiums. The UK has 60+ million people to fill their stadiums. Large metropolitian areas in the US have fewer popular teams. Chicago has 1 NFL team and 3 popular collage teams in their area (only 1 that is actually in Chicago). London has 9 teams in the PL/championship. So the fan base of American football teams tend to be more city and regionally (state) based (commercial on the rivalry between Alabama University and Auburn, two schools in the state of Alabama, whose fans cover the entire state Alabama vs. Auburn Nursing Home - YouTube). Teams in the UK are more neighborhood based. (funny American ESPN commercial on the subject ESPN Commercial | Born Into It - YouTube)
That wound up being longer than I thought it would be...