That's not usually the way that is supposed to work. We expect at least some fans to cheer for the demise of their rival and I suppose the volume of those fans is one way to measure the toxicity of a rivalry, but admins shouldn't act like fans and doing so makes the rivalry more toxic.

Coaches and certainly admins are supposed to think about the big picture, build the programs the right way, and be above the fray...that's their job. President Young, Dr. Hill, Coach K, Urban and KW administered the Utah sports programs like they were fans that wanted nothing more than the destruction of BYU's programs, which is something professionals in those roles typically should not do. It's why teams and coaches shake hands after the game is over (fans do not), because they are supposed to show that it is just a game and competition. BYU admins and coaches in general acted like professionals throughout that time, which is why I attribute the toxicity to Utah.

Admins and coaches shouldn't torch bridges because you often need to cross them later on. Had Utah acted differently the last 15 years then it might have had an ally in the B12, but right now any move to the B12 will be in spite of how they treated BYU and Utah fan reputation (which isn't good among either B12 or P12 teams in case you didn't notice).