I lived in two of those states listed in the mid 70's to mid 80's (one year of high school in Mississippi and my final two years of high school and early adulthood in Arkansas). Both of those states were poor back then and it seems nothing has changed in all these years since.
My father was in the military, so we moved around a lot. The good thing about that is you get to see many different places and can compare them to each other. That is a big advantage over people who are born and raised in one place. How can you know how bad you have it if that is all you know?
Just to give you an example: In our one year in Mississippi, we found out you (parents) had to pay for your children's schoolbooks each year. I don't remember the exact cost, but it wasn't cheap for back then. At the end of the year, you had to turn the books back in. You don't get to keep them, so it's like you're just renting them. In the city we lived in, there was no school bus service (at least for the high school). You either walked, your parents drove you, you caught a ride with others, or you drove yourself. You could get a driver's license at 15 in that state.
Because we lived in so many different places, we knew this was out of the ordinary. None of the other schools we went to charged us money for books and all had school bus service, even if the school was a short distance away. The people who lived there all their lives might think this is the way it is everywhere. They think nothing of having to drive their kids to school or paying for books every year because that's the way it's always been. But hey, at least the sales tax was cheap (3%).
I think this is what the problem is. The people living in those states don't see the problems. They're not willing to invest on improvements that could attract businesses and improve their economy and, at least, bring them up to par with the other states instead of being at or near the bottom. It takes money to make money, but the voters in these states will only vote for someone who will cut taxes. A lot of these voters make very little money anyway. How much lower can their taxes go?