The Ozark balds exist primarily because the tops of hills in the White River Valley have very little soil, as they're made up of dolomitic limestone that dissolves in rain water instead of breaking down into clays. The scant soil that exists is enough to host grasses, but few trees; Eastern Red Cedar can grow, but before widespread fire suppression, it was pretty contained to fire-protected rock outcroppings. With fire suppression (which may have stabilized the soil and limited erosion as well), Eastern Red Cedar and some oaks (blackjack and post oak) are filling in the balds. This is in constrast to the Appalachian balds that are mainly a product of climate differences between the peaks and the lower hillslopes.
The hills to the north of the White River Valley (around Springfield) and south (south of Harrison) are capped by rock layers that have a relatively high clay content and produce soil that can more easily support forests.
The Bald Knobber history is pretty interesting. I had always thought of them as analogous to the earliest KKK (also a Reconstruction-era vigilante group initially) but I hadn't realized until I read the surprisingly detailed Wikipedia page that the Bald Knobbers were Republicans who sided with the North. (Unfortunately, the Bald Knobbers are history at this point, while the KKK is still quite active in the area, especially Harrison/Boone County, Arkansas).