The Rio Grande Valley (McAllen-Brownsville-Harlingen) is, I believe, the only sizable market with no NPR station. Apparently, no public broadcasting entity thinks such a service would be able to generate enough listener support.
In most rural or low population areas, a university or the state will run the NPR station with partial support from listeners and some from the state government. But there are no large universities in RGV. And the State of Texas likely will not step in either.
In Corpus Christi, a non-profit known as South Texas Public Broadcasting runs KEDT-TV 23 and KEDT-FM 90.3. Certainly RGV is part of "South Texas." Could South Texas Public Broadcasting put a simulcast FM station on the air which could cover RGV? Or maybe a few translators, one for McAllen, one for Brownsville and one for Harlingen? I'm sure they thought about it but ruled it out.
I suppose KEDT-TV is carried on RGV cable systems? Or maybe they import KLRN 9 from San Antonio?