I don't know about other situations but when North Dakota State moved up to D1 about 13 years ago it was largely about exposure. The Bison had been successful at the Division II level in the number of programs and that garnered some regional success but given the location of the school the size of the school the size of the Fargo Moorhead community it has long been thought that they should move up to the Division I level and the FCS level with regards to football.
And it worked. Largely on the basis of it's successful football program the Bison brand has become more nationally recognized. Men's basketball's made it to big Dance a couple times As has softball and volleyball but usually they are one and done in those respective sports (the Bison did capture to top finishes in the indoor track national championships this year). But with regards to more exposure more opportunities which translates to more money the move has been successful
Of course it's been bantered around that the football team should move up to a non P5 FBS conference but I think given the demographics of the community the media footprint of the community the size of the region that NDSU is sitting pretty where they're at right now. I think it is also helped that when they moved up South Dakota State partnered with that move and that brought a homemade rivalry and bargaining partner into any conference scenarios that were being considered.And it's also helped that subsequently the University of North Dakota and the University of South Dakota both made a similar jump.
Free your mind and your ass will follow.