I have some very strong ideas about this. Some might even have some merit since I am probably the only one here who has actually played for an NFL supported minor league team. But some background first (for those who might not know the story).
The Atlantic Coast football League played up until 1970 with teams in Quincy (Pats), Bridgeport (Jets), Hartford (Bills), LI (Giants), Pottstown PA (Eagles), Harrisburgh (Steelers), Richmond (Saints), and Roanoke (Washington). Players were made up of guys who had been in the NFL and looking to get back. Some guys who had played at major colleges but weren't drafted, but mostly they were guys like me, fresh out of college, just looking to continue playing.
Everyone was paid. Pay ranged from what I got ($250/game) to a few big contracts. A QB named King Cochran was paid $100,000 to play for the Pottstown Firebirds (or at least that was the story). BTW- Just for reference, $250/game was more than I was making per week teaching school ($175) in 1969. So, while it seems like chump change now, back then it was a decent week's pay.
Our connection with the Pats was that of a minor league team. Our coaches were mostly former Pats players like Bob Dee and Ross O'Hanley. During the season the Pats send players down to play with us. We wore the Pats colors. But we practiced completely apart at Quincy HS and played at their field. From what I recall we probably averaged 10-15K/game. But we weren't well run or marketed. However when we played in PA or VA, we'd get up to 40,000/game. Hartford had a successful operation that averaged between 20-30K
Unfortunately the NFL and AFL officially merged in 1970 and part of that merger was for teams to give up any and all affiliations with any "minor league" teams. Without the monetary support from the individual teams the league quickly folded. For myself, I spent the next two summers as camp fodder with the Broncos. Don't hold it against me, back then, they were a bad team (which is one of the reasons I went there).
But that's just background. Back to the OP. I believe there really CAN be a successfully run minor league system for the NFL. But to keep costs down and the fan base energized it has to be regionalized and branded to a local NFL team. So instead of one minor league, how about four eight-team leagues. They would be centered geographically.
For example: In the northeast - The Pats, Jets, Giants, Eagles, Steelers, Bills and Washington could each sponsor teams. They could set up operations in towns that are nearby the NFL franchises like they did with the teams I played against. Say places like Providence, Hartford, Brooklyn, Pottstown, Trenton, Harrisburg, Richmond and Roanoke.
You'd do the same in a southern region. Another eight in the midwest, and another in the SW centered around Texas.
They'd play a 10 game schedule playing the seven other teams in their division and one game each against one team in the other regions. The winners of each division could play a two-game playoff to see who is the minor league champ. I'd start the season about a month before the NFL starts, The season would be over by the end of October.
You could add a great incentive by allowing each team to add, say, four players to the PS's from their minor league team at the end of their season. Then in March each NFL team would have a right of first refusal to put any of their minor league's team players on the 90 man roster by a certain date. After that they become FA's and can be signed to any team's 90 man roster. Then in June the minor league team's can start signing their own players.
Payment should be very moderate. It shouldn't be considered a full time job. The season, including TC would only be about 4-5 months. Pay them something in the range of $3000/wk including TC. So $40-50k for a job that lasts less than half a year is reasonable for both management and talent. Of course more money is to be made for the teams who win their regions, and for those who get PS contracts with the parent teams
I think the key is keep it local as much as possible. I think there would lots of Pats fans, who don't get the chance to see live games to head down to Providence, Lowell or Worcester to see, a professional football game. with some future Pats players, for $20 bucks a ticket. It would be an excellent training ground not only for players, but for coaches, trainers, and other FO personnel as well.
I think a well run, well marketed team could get 30,000/game in the NE. Down South and in TX they could average 50K. I'm not sure it would be profitable for each team, but benefits to the league and the individual teams should more than outweigh the costs.
The minor league system that I think would fail would be the one where they put 10-15 teams all over the country with no direct affiliation with any current team in the NFL.