I have some quips with your analysis, and I stand by my assessments after many discussions with D3 coaches, most of which were in the NESCAC. Slots definitely do exist, and I have even heard them mentioned by at least one coach at your own favorite LAC. Whether you call them “Athletic Factors,” “slots,” or apples doesn’t much matter. I do agree, however, that it does not matter after the admissions cycle is over what your academic background was in high school. With any luck, you end up in the same place as the rest of the team.
I also agree with @Ohiodad51 that coaches should know how many recruits they have in a given year. Where the numbers get fuzzy is if an athlete is the no. 6 recruit of 5 and the coach wants him or her to hang around in case a recruit decides to go elsewhere, or if an Ivy recruit drops in the coach’s lap at the last minute. The numbers do change as the music stops, and there can even be some horse trading among coaches for extra recruits.
But where does this leave @heartburner? To be sure, the recruiting process requires athletes (and perhaps to a greater extent parents) to learn the system. In the NESCAC, there are a lot of resources. There is the 2014 Amherst Report, the Bowdoin series, the Middlebury and Bates articles, all of which explain the background. There is a Wesleyan article on Coach Whalen when he was coaching that talks about him, but gives a few nuggets about recruiting (like how many recruiting emails he started the season with). Tier One Sports helps on Ivy recruiting. Learn the background first.
Then go talk to the coach. Listen to what the coach says. Ask hard questions. And try to critically analyze not only what the coach is saying, but also what he means. This will not harm admission prospects. It may not help admissions prospects, but I don’t think it would hurt them. Understand that the coach is a source of applications – the more applications, the lower the admit rate, all good for the school. No coach in the world will discourage a kid (any kid) from applying. And, I have never heard of any coach calling admissions to dis an applicant that was not going to make it as a recruit.
A problem can arise when parents and kids think that coach encouragement to apply equals coach support with the adcom. It doesn’t. Because this is the “dance of the tse tse fly,” you need to ask very direct questions like “my kid throws a _____, is that good enough for your team?” "Do you have any open positions on the team for a thrower? Are you interested in my son? Will you give him support with admissions. If you don’t have video to show, some of these questions may be difficult for the coach to answer, but at least ask the coach about the process. If you combine the visit with a tour of the school and an admissions interview, you will be very tired, but you will have a better sense of whether there is any shot for your son to be on the team and get coach support with admissions.
Bear in mind that the level of athlete will be much higher than high school. Here is a story about a soccer recruit at a non-nescac D3 school. Kid: I am on the soccer team in high school. I may not be the best player, but I am very fast and a very smart player. Coach: I am looking for the best soccer player on your high school team. In most instances, recruits put in substantial hours outside of the high school team to hone his or her craft.