You can do anything you want. I don't think there are ever any real hard and fast rules. There are people who are AP-only trained in private practice, just like there are people who are AP/CP in academics. If you are good enough, it will work for you. Personally, I believe in being well-rounded and exploring many areas, but think I may end up specializing as I often like the focus and intensity you get with one specific area.
When you are looking for a job post-residency, it is a good idea to have things to recommend you. Thus, if you are AP only and only know dermpath, your job opportunities will be limited. If you know that is what you want to do, fine. But you better be sure unless you are prepared to go back and do some more training. If you are AP/CP and did a fellowship in surg path and one in transfusion med, you will have a lot more options, because there are several areas you can cover.
Combining AP/CP is only one extra year more than AP-only.