@skieurope notes why this difference exists. The BS needs the athletes to fill out its teams in a competitive way so they recruit. Day schools may not need to do this (although there are some Catholic schools, in particular, that have fearsome teams, especially football!) I think being an athlete can still help – it’s part of who the student is and if they are on an elite track, it will help with college admissions as well – so it’s not useless, but it may be a plus rather than a hook.
Connections matter more at some schools, and are more likely to come into play when there are relatively few seats available.
When you are going through this process, whether for high school or college, it’s easy to feel like everyone else has an edge. All you can do is craft the best application you can. And don’t lose sight of the importance of making a good match in terms of fit. Not all good schools are good fits for good students.