There is an old cliché, “it’s hard to compare apples to oranges”. It's relevant here for this discussion. I've lived in ten different states due to my profession and most of the parochial schools I've seen have been in urban areas until coming here to Nebraska. I haven't lived in Kansas but did a little research.
In Kansas there are 16 parochial schools listed on:
http://www.parochial.com/kansas/list.html that educate through the 12th grade. I don't know what athletic class they are. Of those 16 only three are located in communities of less than 20,000. They are: Pittsburgh, Tipton, Atchison (>10K). Atchison has less than 20K but more than 10K. Or about 19% of the schools from small communities.
In Nebraska there are 25 parochial schools listed. Of those 25 11 are from communities of less than 20K. Lindsay, O’Neal, West Point, Humphry, Hartington, Elgin, Elkhorn, Wahoo, Nebraska City, Falls City, David City. I haven't lived in Nebraska long enough to know if they are suburbs of larger communities or not. The population numbers came from suburbanstats.org.
I feel the size of the community is significant because of the demographic differences in larger communities. In a small community there isn't significant differences in the race, social/economic class, or other factors that are seen in urban areas. In small towns the difference comes from parental involvement. I have a hard time penalizing kids because their parents are involved in their education.
In an urban area there is more of a chance for kids who are good athletes to feel pressure to attend the private school. Many of those pressures are good academics, safer environment, and other factors including I'm sure some that are athletic, but I feel that most are what we all want for our kids. For me penalizing kids in Urban areas because they have gone to a better environment is also not something I'm in favor of.
My background is retired military, earned a teaching certificate, taught full time in a public school in a small town, before going into administration.
Just my thoughts and I know that I only looked at Catholic Parochial Schools not all private schools and that could change the numbers. This is a complicated subject and one that raises passions. The same reason people get upset with officials, they want their kids to have a fair chance and the success of the private schools brings that into question.