This happens to some degree. Residency spots are limited by specialty. Over time, different specialties have come and gone as being extremely competitive.
https://www.ama-assn.org/medical-students/specialty-profiles...
Majority will have a micro, breast or hand practice and have a side hustle in aesthetics so the overall satisfaction stat you’re citing is not reflective.
There are different hassles in cosmetics like increased overhead, patient expectations (which are much higher in cosmetics) and advertising/patient recruitment. Call can be worse as the patient paying $50k for a rhinoplasty expects the surgeon to answer the phone for every whim.