I think there could be a snowball effect down the road. Being good would lead us to be attractive to the Frank Jacksons, Jabari Parkers, and Jordan Bachynskis sprinkled in with one or two good non-LDS players, and then guys like the LP3, Childs, and Baxters we could be quite good. Especially in a sport where you really only need four or five really good players (with solid backups).
But I do completely agree with your point, that our recruiting base is very limiting. I think most fans just wish we could have a couple good years so we could be attractive to those players and that limitation could be turned into a selling point (for LDS star basketball players).
I hope the same thing for football by the way. I think if BYU got the top LDS talent every year, it would be a perennial top 15 team for football and top 25 team for basketball.