I think there are some policy issues that contribute to high dropout rates. Mostly though I believe the problem is not political in nature more so cultural. In many urban African American communities and in many border cities with high Tijano populations I'm appalled at the peer pressure against education. The peer pressure by black males against higher education is a problem. I don't know how many times I've seen bright young African American males mercilessly razed by their peers for being poindextures and orioles when they demonstrated academic success. How thugs and gangsters are idolized over those who seek success in the traditional professions and trades that require an education. I've also seen that in Mexican communities where the value for education is simply not emphasized. "That's for you gringo" is an all to often heard refrain. It also places Mexicans at odds with most of the rest of latin America where there's a huge value placed on education.
Having said that, I saw how conservatives in South Carolina and Arkansas gutted their states public education systems (which weren't all that hot to begin with). When Brown vs Board of education was passed and was supposed to end "seperate but equal" the nebulous phrase, "with all due speed" was inserted. This was interpreted very loosely by southern conservatives as "When were damned good and ready too". The end results was the enforced desegregation of schools in the south during the 70's via busing. When this occurred southern white conservatives withdrew their children from South Carolina public schools in hordes and enrolled them in private schools not accessible to black students while at the same time undermining the tax base for public education in the state with the intent of undermining public education for blacks in the state. No dumber, short sighted and unsustainable policy could have been implemented. In the long term it hurt white children as badly as black as South Carolina is stuck with superanuated school buildings and underpaid, underskilled educators in a broken down public education systems that will cost them a fortune to fix. North Carolina and Virigina though equally hostile towards enforced integration via bussing took a much wiser approach and decided that though opposed, they must obey the rule of law. Those two states have benefited tremendously there by while many other southern states have paid serious consequences for their short sightedness.
I would not live in Arkansas or South Carolina if I had to send my kids to their awful public schools (Thank the good lord I received a good public education in Ohio and one of the best high school educations available in the world in Iowa.).
But one must recognize that the educational problems in the south are not just purely politics. Again cultural values play a huge roll. I don't know how many times in the rural south I've heard comments along the line of "What the hell does that boy need an education for to chop cotton?". There counter part in rural Ohio would have said "I don't care if I got to mortgage the whole damned farm, that boy is going to college!".
So yes, your point is a good one. It's not all politics. Cultural values play a huge roll.