I'm an academic and R1 is viewed absolutely above R2. From a faculty perspective, R1 positions are viewed as much more prestigious than R2 and below. Teaching loads are generally lower at R1 universities and research productivity is higher. Obviously, there's a lot of variation within R1 as well (Baylor and Utah are not at the same level as Stanford or Michigan, for example). But academics have quite a bit of bias and are often the ones serving as reviewers for grant proposals and paper. Achieving R1 status helps to break down some of that bias, leading to more success in research.

I would say that BYU does not have a minimum graduate program. It's decently large.

A point here that seems to be missed is that undergraduate and graduate reputations don't always line up. There are quite a few liberal arts colleges on the east coast that are viewed as very prestigious for their undergraduate programs, but their graduate programs are basically nonexistent. They would not be considered R1 universities. On the other hand, you have "commuter schools" that have large undergraduate programs that largely serve the local population while having a lot of infrastructure built up for doing research at the graduate level. These universities attract the better graduate students from around the world and are among the R1 universities. So large state schools that aren't very exclusive at the undergraduate level (partially at least because they're not supposed to be) can absolutely be very prestigious at the graduate level. And vice versa.