As a non-american, I am baffled by this way of thinking. Higher education is supposed to be a way to ensure that a state is self-sufficient in terms of some core competencies by retaining a small number of workers specialized in compiling, developing, and sharing industry knowledge.
Is West Virginia so empoverished that they can't manage to support the two dozen or so teachers required to support an engineering degree?
There are various regional associations to address this sort of issue. A college friend, a Virginia native, wanted to pursue a master's in library science, but Virginia did not offer one. North Carolina did, and so through one of those multi-state compacts, he went to UNC and paid in-state tuition.
We don't expect towns of 2000 people to support a high school. They go to a regional school - perhaps only one high school per county.
Tennessee is legally divided into Western, Middle, and Eastern Tennessee. There are a lot of rules in the state constitution that respect these Grand Divisions; IIRC an equal number of TN Supreme Court justices must be from each division, etc.
Anyway, the University of Tennessee is in Knoxville, which is in the Eastern Division (and a long way from Memphis). The University of Mississippi, in Oxford, is only about an hour and a half away from Memphis. For many years, students living in at least metro Memphis (and possibly most of Western Tennessee) could attend Ole Miss and pay in-state tuition - which is why in The Blind Side, the family were Ole Miss supporters. Memphis is the cultural capital of the Delta region, which covers parts of Mississippi, Tennessee, and Arkansas, and Ole Miss (though not in the Delta) was the natural flagship university for the area.
Tennessee just paid Mississippi for its students. It was cheaper than building another university that would only have attracted students from a relatively small portion of the state.