In any area like this you are going to get some sort of bell curve, even if it looks like a bell that’s been run over by an Abrams tank.
From my perception, advancing the kids grade-wise is an ego achievement for the parents, not a real benefit to the child. If the child is that bright they should probably be given the opportunity to advance their intellect outside of their school age grade.
These days, sending a 15 or 16 year old off to college is probably not a wise idea. There are too many social elements involved. They would be better off getting personal tutoring and staying in the family environment while associated with people their own age. This is particularly true of boys.
Parents need to realize that education isn’t a race, it’s a process. So what if your kid can read at 3 and gets into kindergarten at 4? Have your kid graduate from high school at 16 and then deal with the challenge of what to do with him. Do you want him living in the dorm with a bunch of 18-20 year olds?
Back to the OP, I too would like to see some empirical studies.