presumably due to the demographics of the kids that play the sport. About half the top programs are elite universities similar to ND. I also don't think it's all that much of an issue in hockey because hockey has high scholarship limits. It seems like it could be somewhat of an issue in soccer, especially mens soccer which has lower scholarship limits, but private schools seem pretty well represented in the top 25. I again think this speaks to the demographics of who plays soccer in this country, although I suspect that's changing rapidly.
I suspect it hurts the most in baseball and track.