I think the OP is analyzing things from a pre-med perspective without spending too much time in an actual FP clinic.
There are tons of patients going to the FP clinic because of pain (back, elbow, and particularly shoulder). My preceptor used OMT on all cases, in addition to the usual medical therapies (pain meds, steroid injections).
Most people don't self-refer themselves to a "pain clinic" because most people don't know the source of their pain. In other words, if your shoulder hurts after a game of softball, do you set an appointment at a pain clinic or do you go to your FP to see what's wrong? (bursitis, rotator cuff tear, etc.). You might not necessarily need any treatment beyond rest and OTC anti-inflammatories / analgesics.
Long story short...musculoskeletal pain is one of the top reasons why people see FPs, and OMT fits in very nicely in the overall pain management strategies.