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.