Texas does have desert. About 10% of the state is desert, specifically the Chihuahan desert, the largest one in North America. I'm a 6th generation native of the Hill Country, and its very far from desert as you said. Primarily oak and juniper woodlands and grasslands. Surprised you picked the Hill Country as "the closest to a desert" when the Llano Estacado and Permian basin are much more arid and devoid of trees and other vegetation.

I agree with everything else you said. Texas has bad PR, and a hostile gov that hates everyone here, especially their own base.