I put my feelers out to get some answers to the questions mentioned above, and this is what I know so far.
DPS Dispatchers have a Harris console in their office to talk with LPD, LSO, and all of the different school districts that operate on the system. DPS 105 (helicopter) has a Harris mobile programmed to 'nearly everything in the area'. It is understood that some supervisors may have Harris mobile radios. Other than that, I would assume that it's cost or politics that keep them from operating on the local system. Perhaps if it were regional they would participate?
As far as the operations at the Frenship incident, it certainly sounded like it went smoother than previous large-scale incidents in the past, specifically the Airport Disaster Drill and the TTU shooting. LPD still likes to operate on their own secure channels, but they did have a unified command with LSO, FISD PD and DPS, so comms seemed to flow more evenly.
South Plains IMT talkgroups are primarily in LPD and LFD radios, and some other city employees. Most radios on the system, if not all, have access to most of the ICS- Task Force channels, while supervisors have access to the ICS-CMD groups. I can probably put together a better radio layout if anyone is interested.
@TwoByTwo, most agencies fall back on their own policies and procedures (and training) and operate on agency-specific talkgroups. It's still pretty hard to get them off local TGs and onto interop TGs.