However, I don't think the reasons for BYU's growth and prominence involve the honor code.

It's grown because the LDS church and culture puts great emphasis on education and personal development. So as the church grows, you get more and more kids that value education and excel in school. With only one church school (there are more now as you mentioned) to choose from, it's only fitting that the academic standards will continue to increase as the LDS population goes up as well.

BYU has grown and strengthened in spite of the honor code, not because of it. I know people who didn't go to BYU because they didn't want to deal with it. As an easy example - and you're welcome to call it a humble brag - I was accepted with a scholastic scholarship and chose not to go. The honor code wasn't the only reason, but it was part of it. I had a bit of a hard time coming to grips with the fact that as a 19 yr old living on my own, I would have been facing stricter rules than a high school teenager living at home. And yes, my parents were pretty strict.

That's not to demean people who think one way or the other. It's a choice. To some it's not a sacrifice at all to comply with the honor code, for others it's harder. That doesn't make one person better than the other, as I don't ever recall the honor code coming up in a PPI, temple recommend interview, disciplinary council, etc. Overall, I feel BYU would be just as good of a school and a good environment for young people without the HC. But it's working and obviously neither the Brethren nor the school have felt the need to change it, so it can't be that bad.