I don’t mean to dismiss the central question of the post title in any way, since retention of single youth (16-30) is a serious issues in the Church (70% inactivity among young men prior to missions is a pretty good estimate), but just a few things to consider for historical context:
1) This has been a serious issue since the beginning of time – and has relatively little to do with the apparent “righteousness” of the parents. IF we take the scriptures literally, Heavenly Father lost 33% of his youngsters – and Lehi lost 50% of his kids who weren’t born in isolation – and Israel never could keep those darned rising generations in line – and Alma’s and Mosiah’s sons were radical sinners for a time – and pretty much every generation who lived a near-Zion state lost it to a new generation – and the activity rate overall in the Church was far worse a hundred years ago than it is now – and the same issue is worse in most Christian churches now than in the LDS Church.
2) Those who leave home tend to stretch and test the boundaries anyway – and those who go to college where there is not a church within easy walking distance or an active, engaging Institute program slip into inactivity almost naturally.
3) It’s hard to gain a truly personal testimony while remaining in the presence of one’s parents and childhood leaders – and our pre-mortal life narrative acknowledges that fully. Thus, it’s rare that a young person really has a rock solid, personal testimony. That kind of faith needs to be grown and gained on one’s own – at the very time when the challenges are the greatest.
4) Most of the “issues” everyone mentions simply are the vehicles our current youth drive on their way out the door. Other times had other vehicles.
I don’t have any easy answers – but my main suggestion would be to give our youth the responsibilities and power they are supposed to have within the YM & YW programs. See them and treat them as young MEN and WOMEN from the age of 12 – which really doesn’t happen very much, in my experience. Our society has infanticized the teenage years to a shocking degree – and we buy into it too much, despite (not because of) the Church.