I don’t know the answer to this but are the schools whose AD’s are actually bringing in big money struggling for funding? For example Michigan, texas, bama, and OSU are in no way struggling. The schools who seem to be struggling are the smaller ones who’s AD probably isn’t making that much to make a difference.
I think in most cases the impact that athletics could have by kicking back money to the university isn't nearly as big as people think.
That's not to say there isn't a lot of waste and some really poor ROI on a lot of athletics facilities renovations, because there are. For most athletics are <5% of their total revenue. Ohio State is like 2.5%. Plus a lot of that athletic revenue is donor money that has an intent tied to it.
But to your point, The total Alabama system's endowment is $1.8B, which includes Bama, UAB plus whatever other state schools they operate. I think Alabama itself is like $1.3B. ISU's alone is over $1.5B (U of Iowa is $3B). Bama also has seen a decrease in tuition revenue over the past couple of years. So I'm not sure if they are struggling per se, but Bama might be a school where they AD is raking it in while the overall university is not.
But generally I do think there's probably a pretty good correlation between overall school and AD financial health among schools at least in the Big 10, Big 12 and SEC.
I know, totally shocking that Alabama might be that way.