I assume that your questions refer to private autopsy services that hire per diem pathologists to do private cases requested by family members. Essentially these services are contacted to do a case by a family member when they are unable to have a hospital take on the case and the local ME has declined the case. If the family is willing to pay for a private autopsy, chances are high that they have litigation in mind and you have a high likelihood of being sucked into their litigation. Rarely is a family member willing to pay the high fees for a private autopsy just because they have a curiosity to know what a loved one died. Bottom line is you better be very comfortable dealing with lawyers and all of the baggage that comes with litigation, as Mike Sheree has alluded to. Getting paid by lawyers is often problematic as well. Not infrequently I have to send out 2-3 invoices and wait upwards of 4 months to get paid. I only get paid on the first invoice when a deposition is upcoming and they are forced to settle the bill if they want me to proceed with the deposition, so yes it is frustrating.
As to work/life balance, I have been doing both SP and forensics for close to 25 years and only know a very small handful of FPs that do private cases on a full time basis, and they almost all exclusively involve litigation and these docs are not well respected in the FP community. I personally would not want to be at the mercy of lawyers over the extent of my career by just doing private cases. Most of my FP colleagues only take on a handful of private cases outside of their normal FP workload.