The NFL did try a minor league for awhile with the World League of American Football when they bought it and only kept the European teams. They would send over some of their less established players in the spring to play. Just didn't catch on enough to be profitable. Most other leagues that have tried to start up as a sort of minor league have failed over the years: UFL, XFL, WLAF. Arena Football is about the only thing that has succeeded, but it's also not really typical football either. Problem is that if you aren't making the NFL out of college, you probably aren't going to be in it long term so the fans aren't really interested. Of course, none of them were leagues that tried to attract college aged players.
In baseball, the minor leagues were setup a long time ago, independent of the major leagues so most clubs have a long history with the cities they're in. It wasn't until, I believe the 50's-70's that the major league clubs started setting up the current minor league structure. What makes them profitable now is that fans are attracted to the fact that they might be seeing future stars or even older MLB vets play as well as the fact that the Major League club is paying the costs and per diem of almost all the players.
Which kind of goes back to why a minor league would struggle to be financially profitable in this climate. With college football being the money maker that it is, the best coaches, strength staffs, etc are already taken. The best players not only want access to that, but also access to millions of viewers to build their brand so that they can make the money once they are able to be drafted. The NFL doesn't want to change things up because they don't want to have to be responsible for the costs of keeping thousands of players healthy, feeding them, etc when colleges are already doing it for them. On top of that, under the current climate, if an 18-22 year old gets hurt and can no longer play, at least he is still getting an academic degree that he can fall back on.
I think Mike Shanahan was working with some others on trying to set something up in California last year that would kind of be a prototype for a minor league system. Haven't heard much since the announcement other than it was supposed to be a 4 team league for players 18-22 that didn't want or couldn't go to go to college. I believe it wasn't sponsored by the NFL, but they are keeping a close eye on it; there is a group of NFL coaches and owners that want to have more control of the development of players coming into the league, especially with the advent of spread offenses that don't translate to the NFL. Possible that 10 years down the road, it becomes something.