I think BYU has a chance with most Polynesian and LDS athletes, but I don't know if BYU is the right place for everyone.
I think BYU offers Polynesian athletes something they can't get at other schools--a chance to play for a Polynesian head coach. For Samoan and Tongan athletes he's a very positive role model--proof they don't have to be wearing football pads to achieve success, and that they can reach the top of their profession whether they're holding a clipboard on the sideline, being an elementary school principal, or holding a scalpel and wearing medical scrubs. I can see a lot of kids being drawn to that and wanting to help make him successful.
At the same time, not everyone is destined to attend BYU. For non-LDS students, living an honor code lifestyle can be hard and you can get kicked out of BYU for doing things that would be considered normal and healthy at other schools. LDS kids might feel like they get more exposure playing for a different coach, or that God wants them to be a member missionary where they might have a lot of influence.
As a BYU fan I'll miss out on seeing them play, but as a fellow child of God I can appreciate their agency.
While I think BYU has a chance with top athletes, I don't think it's necessarily a failure for BYU if a talented player goes to Oregon, USC, Alabama, or even Utah.