Big-city hospital laborist physicians need the skills and experience to do hysterectomies, gyn (ectopic, ovarian torsion etc.). For low-risk deliveries, most facilities will hire a CNM midwife instead (because they are popular with pts and cost less).
Even an FM doc with CS fellowship training would not be hired as a laborist in a big hospital. But you could be hired to provide locums FM/OB coverage for a rural hospital that needs weekend/vacation OB coverage and possibly CNM backup. There, the FM doc can cover both mom and baby so we are more in-demand than an OB who can only cover mom. For those jobs, you must have C-section training and experience. They exist in the rural areas of the midwest (e.g. KS, NE)