I'm wondering what they have in common with the schools you named other than geography and lack of local talent
That would be the connection. Virtually all of the top teams in football, year in and year out, have a large pool of local talent. That's why you find teams from the West Coast, Oklahoma-Texas, Florida, and the SE in general, plus Ohio State near the top, and why you don't generally find teams from more rural states.
Once in awhile a team from some other area can pop to the top, but it's usually temporary. Nebraska was able to stay near the top for an unusually long time for a team from an area without the same type of local talent. It's particularly unusual because they not only don't have have sufficient local talent, but they also are not an easy location to recruit to. ("Come see, umm, the corn..???)
The one thing that does separate them from the other teams in the plains area is that they used the money they got from their long string of success to build some incredible facilities, and that does add to their recruiting appeal. They also have built a tradition of Academic All-Americans, another recruiting appeal. Together those help them stay above other teams from the area, but how far above them?
When I think of Nebraska fans, I think back to one delusional fan who told me back in 2003 "We aren't unreasonable. We don't expect Nebraska to win the National Championship every year, but they should at least be playing for it every few years."