three broad evolutionary stages.
The first stage, which I will call the "foundation stage," went from its founding in 1875 to the 1950's. BYU was basically a backwater institution during this period. The church didn't invest much in BYU prior to the 1950's, in part, because the church's resources up to that time were so scarce (for a good part of BYU's early years, the church was barely solvent and then the Great Depression happened, followed by WWII). Instead, the church relied on the University of Utah and, to a lesser extent, Utah State as somewhat "de facto" church universities, which schools the church influenced far more than it does today (and up until about the 1950's, there were still a few people around who were alive when the University of Utah was church owned). Think about it, how many prominent LDS (e.g., general authorities, etc.) born before, say, 1930 can you think of who attended BYU?
The second stage, which I will call the "growth stage," went from the 1950's to the early part of this century. This is when BYU really came into its own as a university. During this period, the church invested a higher percentage of its resources into BYU than any other time. Most of the buildings on campus were constructed during this period and enrollment grew by probably something close to an order of magnitude. At the same time, the church wasn't yet so big that BYU needed to be super selective as to who they admitted (at least until the latter part of this period). This was really BYU's heyday or "golden era" as the church's school and a higher percentage of active LDS kids went to BYU during this period than any other. Simply put, during this time, BYU was "the place to be" more than it's been before or since.
The third stage, which I will call the "maintenace stage," stage has been going on for a few decades. Somewhere along the line, I think church leadership decided that they weren't going to invest as high of a percentage of their resources in BYU as they had during the latter half of the 20th century. Instead of continuing to grow BYU, they decided to more or less maintain it, partially because: (A) there's only so much physical space for BYU to grow; and (B) the church was finally large enough to have strong institute programs at many other universities. So investing heavily in BYU took a relative back seat to other priorities (such as making temples more accessable to more members of an increasingly international church). This naturally led to increasingly stringent admission standards, which I believe, has also contributed to stricter honor code enforcement. Now, instead of being the church's school for everyday LDS kids, BYU has become the church's school for overachieving LDS kids (average Joes need not apply).
IMO, it's not conicidental that we've seen a decline in BYU athletics (at least in the two sports that matter) during this third period. Then you have other aggravating factors, such as the University of Utah being admitted in the Pac in the midst of the church going into a maintenance stage with BYU (as well as shifting socio-political and intercollegiate athletic landscapes that increasingly disfavor BYU).
Then, as far as football in particular goes, BYU kind of caught lightning in a bottle for a while with a legendary head coach who employed a novel passing game that hardly anyone else ran at the time (with an improbable succession of NFL caliber QBs to run it). This just happened to occur at approximately the same time BYU was in the zenith of its heyday as the church's university. A lot of us are living off the fumes of those memories.
Finally, the point of this post isn't to let our current crop of coaches off the hook (I think we can all agree that BYU's ceiling in both major revenue sports is markedly higher than what we've witnessed in recent years). But I think it's important to include BYU's evolution as part of the conversation.