Someone can correct me if I'm wrong, but I don't think preferences have anything to do with the minimum amount of AP needed to unlock a scholarship offer -- that's entirely arbitrary and pre-set so Player A might require 70 AP's to unlock the offer while Player B might require 125 AP. Those numbers will be consistent for all users, regardless of preferences, and are completely random, aside from we've been told that high-star recruits likely require more effort than your "Average Joe" (no pun intended...)
I think the preferences specifically come into play on subsequent actions and the calculation for who is "in the lead" -- an HV has more value to a coach with 2 Very Good preferences than it does for a coach with 2 Bad. The 400 total AP you've invested in the player will carry more weight in the interest level calculation than the 400 AP of someone with a poor preference match, etc. I don't think it plays a role in the point at which two players can offer a scholarship though. And if I'm wrong, someone please correct me because I've been viewing it wrong the whole while then!!