I trained at a "prestigious" institution with a strong academic and research focus. Many residents chose AP-only or CP-only tracks, and some residents who started out AP/CP dropped the CP portion during their training. This is a choice that I do not endorse.
For starters, CP was one of the highlights of my training. It was intellectually stimulating and satisfying in a way that AP never was. It reconnected me to the basic science underpinnings of medicine. I felt like a medical student again which was awesome because I loved medical school. And my program offered a particularly strong CP experience for those who chose to take advantage of it. Although I do not have first hand experience at MGH, I am inspired by Dr. Laposata's vision of what clinical pathologists can contribute to clinical care. We sometimes participated in multidisciplinary rounds. We attended clinical patient care meetings. We were able to provide a lot of leadership and advice on difficult patients, to improve laboratory utilization, and put an accessible face to the clinical labs. I felt like a real doctor! CP was awesome at my institution and by skipping CP, I think residents cheat themselves of one of the most rewarding training experiences of their careers.
Secondly, CP provides a nice respite during the training period. Although there are long days on CP heme, the schedule is light compared to AP (and nothing compared to internal medicine, surgery, or pediatrics residencies). It's kind of like how some surgical programs take a two year research break in the middle of training. Some residents have children during this time. While there is no easy time to have children, during your CP years is probably as good a time as any. It is also a good time not only to aggressively immerse oneself in CP, but also integrate and mature your AP knowledge. Most of us at my institution followed up our AP/CP with a general surgical pathology fellowship which was the single best experience in my professional life. But I know that I'm a better surgical pathologist because of my CP training.
Finally, being AP/CP opens the most doors in private practice. Yes, many AP-only graduates have successfully found private practice jobs but they are the exceptions. They have found niches where specialty training and/or geography made them an invaluable asset to a group. But the value provided must overcome the disadvantage of not being able to share CP call or direct portions of the laboratory. Providing value is not, "I'll gladly do your GI biopsies, but I refuse to do Pap smears, look at body fluids, or take any responsibility for transfusion reactions." Providing value is, "I'm great at all aspects of AP, particularly GI, but I also have interests in QA/QI projects, interdepartmental infection control policies, and improving blood utilization." The main bread-winning function of a private practice pathologist is surgical pathology. But in my opinion, the best additional training you could do to improve your job potential is CP. Then after that, a general surgical pathology fellowship and/or subspecialty AP fellowship.
You should skip CP if you absolutely HATE it so much that you'd rather pass on a sweet job if it required CP. But even if you're going into academics, I have never never heard anyone regret doing CP (even if they do not use it in their current job). I have heard many people bemoaning and regretting not doing CP.