We definitely hope we can see a significant boost in our recruiting just from being in the Big12 but our foundation will always be LDS players (whether in Utah or other states).
As for the requirement BYU needing Utah to produce NBA players, I don't think that's a huge issue. We do need guys who can do as you say, help us get to the tourney and win games but In looking through Big 12 rosters last season (2021-22) there weren't a lot of NBA guys on rosters. Baylor had 2 guys on their roster make the NBA, Kansas had 2, and TT/Texas/OSU/TCU/ISU/OK/KS/WV all had 0.
LDS players will always be BYU's recruiting foundation and we can get to the NCAA tourney with that, as we have in the past, but we will need to augment that with some elite talent that we haven't normally been able to attract if we want to be competitive. However, getting the best LDS players will be important.