I'm going to make the assumption you are a male when I respond, so bear that in mind.
23min for a 3mi/5k is probably designed not to weed out the "untalented" so much as it is to weed out the unprepared. I can't think of any high school freshman boys who could not run ~23min in the 5k so long as they ran a couple miles a few times a week over the summer. That doesn't mean those boys don't exist, but I think their appearance is sufficiently unlikely so that making a cutoff of around that time is most likely going to weed out a lot of lazy kids and close to 0 untalented but passionate kids.
That being said, I'm not really into making cuts in high school cross country. You never know who's going to catch fire, or, running aside, who will end up benefiting the most from the discipline, camaraderie, and work-ethic sport can instill in adolescents.
I liked my high school track coach's solution to this dilemma: his roster limit was due to the number of uniforms he had to distribute. We always had a lot of kids trying out, and his logic was that anyone who made the team should get a uniform and be able to compete in at least the handful of home meets/close dual meets. It's not a perfect solution, but it kept the numbers somewhat practical (~80 kids, I think) without losing too much in terms of cutting.