BYU currently competes with other R2 schools for grants. They do very well against those institutions. If BYU becomes a R1 school, their professors now are competing with the likes of Stanford/Harvard. Most professors do not want to. BYU cares (they love their research as much as anyone) but doesn't want to care enough. I think BYU would do well as an R1 school (aka adding a medical school), but it would need to either clean house of some of the professors or expand their graduate schools to bring in more PhD students to increase the quality of research being conducted.

Most R1 schools are R1 because they have a medical school. Utah's research money comes mostly from their med school due to both med students, residents and PhD students.