You know, normal children being taken to a Pediatrician is only a recent phenomena in the U.S.
Historically, only 'sick' kids were seen by Peds MDs: kids with life long conditions like diabetes, epilepsy, immune compromised, etc.
Family Docs and General Practioners are quite competent at seeing the entire family. Many even deliver baby's, so no need to even go to an OB if you're all healthy and comfortable with that choice.
But with our litigenous society and all the mal practice lawsuits over doctors not catching something early enough, many healthy people have flocked to specialists as their primary care physician.
In my experience, one of the benefits of a Family Dr. is that they maintain a life long perspective on the phases of our lives and are usually not as quick to label people and kids.
We have used all: Family Mds, GP's, Pediatricians,Dermatologist. I personally use an Internist due to an accident I was in, but would be very comfortable with a Family MD.