Baseball (MLB) has a minor league, Hockey (NHL) has the AHL, Basketball (NBA) has the D-League, and even Soccer (MLS) has the USL and NASL although they may not be farm leagues in the same sense as the other sports.
It could be argued that NCAA college football is a developmental league, but that alone does not explain why there is no professional developmental league for after college since all the other sports listed above have NCAA college leagues and still have a farm league.
There are a few differences between American Football and other sports that lead to this: particularly, the length of playing careers (shortest by far), and the cost of running a team (largest by far).
NFL teams are very large, with 53 players active of whom 46 play on any given Sunday, and every single one is typically utilized except perhaps a backup QB - compared to a baseball team (25, of which 12 or so play most days), hockey team (25), or basketball team (15, of which many teams use single digits in most games). Assuming a true minor league existed - where the game was played the same as it is at the pro level, which is fairly important for the minor league to have value - you'd need similar roster sizes, certainly at least 40 per squad; that would cost a lot of salary.
Football also is the most dangerous of sports, which means it would have substantially higher expenses for doctors and health insurance; it also probably would need to pay players significantly more (minor league baseball players make very little, so a minor league team is pretty cheap - lots of players who have no shot at the majors, just filling spots, at $30k a year). If it were a true minor league, with nearly NFL size players (so 280-300 lb offensive and defensive linemen, etc.) you'd need to pay people appropriately. Semipro football is a thing and people certainly enjoy playing it for very little or no money, but they're not playing at the intensity and with players of the size of NFL players. You wouldn't be able to get away paying people peanuts.
The current Arena Football League, which is not really a minor league - the size isn't comparable - pays about $15k in salaries per player; but the talent level isn't nearly the NFL level that it would need to be. The earlier Arena league, which did have close enough to NFL talent that it had some elements of a minor league system (ie, it wasn't uncommon for good Arena players to go to the NFL), paid much more - 31k minimum, 80k average. They also went bankrupt quickly. The current one is doing better, but even now isn't entirely financially sound - and that's with a lower quality of player at the lower salary level. The CFL pays about 80,000 a year, which is probably the only league that can truly claim to be sufficient quality that it could fill in as a minor league system directly.
The NFL does have the practice squad, which serves some of the purposes of a minor league team (ie, some talent that they work with regularly to learn the systems, and can call up to the main team when someone gets hurt). I imagine the size of that squad (8 players) is well defined by the actual needs of teams - if everyone needed more, they'd increase that size.
All of this is notwithstanding the fact that there have been multiple attempts to sell smaller leagues as NFL minor leagues. The USFL tried in 2012, now the FXFL is giving it a shot... who knows what will happen, but I suspect the same as in the past: a few years of failure followed by league closure. College football and NFL football just are too successful right now at chasing viewers to lose out to a new minor league. The major attraction of minor league baseball is watching professional baseball in your home town - and colleges provide that for football.
Money.
If the NFL wants a farm system and there is a good chance they will in the future they will end up footing the bill for a lot of the infrastructure/costs.
I have had offers to play in an older version of arena football and that included a per diem and $250 a game. I am not sure most current arena league players get paid more than 20-30K a year if that. So the choice was easy for me, stay at my tech job. So right away to get a higher quality player the league will have to be able to pay players something more than minimum wage. Also note that since almost all good players will opt to go to college right now (this could change) for football experience, that your player pool is 22-30 year old. If I was 19 and was offered an arena league spot I would have taken a pack of gum. At 24 with a real job there are ramifications to quit your job (to make practices) to make almost nothing. Baseball and hockey have a lot of teens and very early 20s in their pool. While football might have these ages too, the best out of this group will play at Alabama or Ohio St.
A small football team (11 on 11) would need at least 35 players to function. This is usually the case in semi-pro leagues I have been involved in - which are nothing but regional clubs that play each other. There are several leagues like this in the midwest. There are "tryouts" but usually anyone is accepted at a practice given they don't get in the way. Some teams just need warm bodies for a scrimmage.
And then a coaching staff for football is usually a lot bigger than other sports. You would have at least a head coach, 2 assistants, and trainer on staff. This is the bare minimum.
The only sport that comes close to football as for equipment costs is hockey. With the concussion issues I have seen equipment prices go up 3-4 fold for organizations the past few years. Not only is stuff more expensive but the stuff expires and has to be replaced more.
And then the biggest hurdle is facilities. Baseball stadiums are multi-use venues, support tons of games (colleges usually share), and are not real expensive. Hockey arenas are more expensive but offer a great fan experience with the fans sitting on top of players and the arena atmosphere support a lot of concession sales. The NBA D-league is losing money right now but they are using shared arenas, (I have not heard of an arena being built for the sole reason of a D-league team), hardly any equipment costs, and the players make very little.
So with the costs associated the only thing that compares with football is hockey. And hockey has three intrinsic advantages. It has younger player pool, it has a different in-game atmosphere, and a biggie is that Canada and the northern US is hockey crazy with little competition. (Note a fourth that was brought to my attention is that hockey rinks often are used almost 24/7 in the minors for ice time, adult leagues, ice shows, and so on)
Football will have to find some way to play games in places that fans want to visit. Indoors would be preferable but fans and the NFL probably are going to want a standard field. These teams really need to be in cities where there isn't great sports competition and the only venues indoors are mainly in the NFL - a few colleges might be able to help out here. Also the intimacy of the experience is off putting 10K-15K fans in a stadium that holds 70K. Same holds true putting the games in a college outdoor stadium. Just no real answer for the facilities issue that a minor league football system would face and really the reason for so many minor league football failures.
The only answer is for the NFL to step in and build a few stadiums using the same kind of slow build style that has been used for soccer over the past 10 years. In fact they might be able to use some of the newer soccer stadiums. It is a given that a football team would start its season in the winter or spring so there is a lot of chance for sharing stadiums but even if they have shared stadiums that have little upfront money, there will be losses for years until there is a fan base to support these events.
Note: That if this happened that the NFL draft would have to have a complete overhaul. Actually the whole player acquisition process would have to be overhauled too. So first the draft might have to go 20+ rounds to support a team's ownership of a minor league player. This would mimic baseball/hockey and would really be a different.
Second NFL teams rely on being able to pick up players when theirs get hurt. A lot of times the player is on another team's practice squad. If teams had minor league systems they would own practice squad players. You could say that well a team should have backups on its minor league team... Well if 4 offensive guards go down, what if a team doesn't have enough? There could be situations where a team could get a practice squad player from another team at the guard position and he is the best guard not on a roster in the NFL, but if that team had a minor league system their guard might be the 500th best not on a roster... No answer for this but this would have to be greatly changed.
The NFL used to operate its own developmental league in the USA and Europe between 1991 and 2007. It was initially called the World League of American Football with teams in both the USA (including non-NFL cities like Sacramento and San Antonio) and in Europe. After a few years during which the league was on hiatus, it returned in 1995 as an all-Europe affair. In 1998 the league changed its name to NFL Europe and operated up through 2007. The fact that the NFL currently plays one or two games in London each year is a remnant of NFL Europe.
When the league was operating and playing games in the spring and summer, NFL teams could assign several young players over to develop. While this was a good idea on paper, I remember that the players that did get sent over were generally borderline/fringe players, typically those that are cut after the final preseason game. So basically, the players who are on today's NFL practice squads are those that would have been sent to NFL Europe. The good rookies (like 1st or 2nd round picks) were kept on the NFL teams' rosters.
NFL starting quarterbacks who played in the World League/NFL Europe earlier in their careers include:
While I cannot elaborate directly towards your question about a farm league for the NFL, there are still many indoor and Semi-Pro leagues out there if you are interested in a side bar to lower level leagues that might interest you or others reading this great post.
Here Wiki has a great list of American Football organizations around the US and Canada that are both professional, Indoor and Semi-pro.
Read up on these leagues now, because who knows maybe the future will change and a couple of them will become farm leagues, or maybe not....
Of all college sports in the United States, football is the one that most resembles a professional league. In many ways, the NFL relies on colleges to act as their farm teams. The downside of this approach is that the teams cannot train players into their systems like European football academies tied soccer teams do. The upside is that fans pay way more attention to college football than they do baseball, hockey, or basketball's (relatively new) minor league programs. This way many football players are recognizable stars before they are even drafted by an NFL team.
