I think it could create the chance of RP, however, at the moment, meeting up with a Physician or Doctor type is largely based on whom is available at the time. People have expressed agitation when things take longer. And my personal concern is that if people start choosing out of the way locations, and whom is available during their play times cannot easily get to to those spots, that creates resentment.I frankly like the idea of being able to choose a location to be transported to, as ultimately it creates more opportunities for rp.
Myself? I'd say the Madison by default, and otherwise make it based on where the injury happened. Or incorporate the new carriages and charge more for going farther. Or ... make the choices and pick-up speed based on the Health Metric.
I'd also argue that injuries serious enough to send someone to a Clinic, should ping Reeves (in appropriate areas, Metrics based) as well as Physicians. If you walk by normally and are bloody, NPC Reeves comment. So you'd think they'd pass it along. As that would also encourage RP. I'd argue so would a policy about making rumours if you are brought to the Hospital.