I will, at my peril, weigh in on this yet again. The determining factor is not the number of enrolees, it is the fact that state schools, by their very nature and purpose, are, and should be, less discriminating in their enrollment. Their charter is to educate the masses (not exactly stated, but that is the gist). Therefore, a student who would probably not make the "cut" academically for a private school, whose standards are routinely higher, will be able to get into a state college. That's not disparaging those students. If my memory serves, Bill Gates is not a college graduate. That means that an elite athlete, who might not have been as diligent in his academic endeavors in high school has a better chance of getting accepted at a state college than he does of getting admitted to a private school.
I've tried to get this point accross a number of times, but have been ridiculed, usually not addressing that specific point. I hope I have better luck this time. It's not a guarantee that a state college will have more, better athletes, but it is an advantage they have. Another adavatage is lower cost. As has been pointed out many times, private colleges probably give out more financial aid than do public schools (although I've never actually seen the stats on that, I don't dispute it), which might somewhat offset that advantage. There are many other factors, but to deny what I have written above is dishonest.
No it's not dishonest to deny what you wrote, it's simply disagreement. There are a lot of private schools in D3 with ridiculously low standards. If you can breathe and write your name on a check, and have a high school diploma, there is a private D3 school that will accept you. While public schools certainly have lower academic standards, and for good reason as you point out, then the elite D3 private schools, D3 is a huge universe and there are more than a few diploma mills.
I will agree that most private schools cannot compete with in-state tuition for a public school, even with a huge financial aid package. But there are exceptions to this as well. Many private schools can offer full-ride need or academic packages, or, as W&L just went on record with, full tuition for any student whose parents make less than $70K. Of course you have to be somewhat in demand to qualify for these packages, usually the better students, who may or may not be athletically inclined. I won't deny there is an advantage to a moderately above average or lower student from a moderately above average income family or lower in attending a state school.
Overall though, the argument is not particularly strong.
Especially with Mount Union, a moderately expensive private school, as the longtime heavy weight in D3 football. Only 1 public school made the elite 8 this year. If there was that much of an advantage, more of the scattered public schools would have progressed, even accounting for the fact that the public schools are primarily grouped in just a few conferences. On a larger basis, the vast majority of D3 dynasties, soccer, swimming, wrestling, etc., all belong to private schools.