Majority of ex pros in the NFL and NBA have actually had a good education on top of their sports careers.*
*I'm aware many of them have degrees handed to them on a plate but you'd think they're not the ones who decide to go in to punditry.
A couple of things to note:
1) Former NFL/NBA players are going to be pretty knowledgeable because their focus is on those leagues which are pretty insular. There are no rival leagues of comparable strength. The NHL has players from several different countries, as does the NBA. The NFL less so.
Maybe, a former NBA player will know something about college basketball (and even more rarely about Euroleague) but they probably won't be dealing with much coaching/player turnover outside of the off-season
2) They may come across as better informed, because those sports (partcularly NFL) are more tactics driven which requires a better knowledge set
3) The draft is a big thing in North American sports and requires an entirely different set of skills. Consequently, many prominent NBA, NFL and NHL broadcasts will have a non-player who understands that world (often a former GM or broadsheet journalist)
I'd actually argue a lot of the football coverage from former players is similar to MLB, where you have the split between those that shun stats and modern tactics and those that embrace them. A lot of PL pundits who were former players started their careers before the influx of continental methods (stats, tactics, sport science) and perhaps that has shaped the backwardness of some of their ideas. Also, I think there is a certain myopic element that exalts British uniqueness and separateness from the continent, which is perhaps also influencing their approach.