I think that the rivalry game benefits Yewtah more than it benefits BYU.
I also believe that a significant portion of yewt "fans" only cheer for the school because they hate BYU.
Similarly, I didn't "hate" yewtah until I went to BYU. Don't get me wrong--the rivalry game is fun...but I really started to realize how ugly and personal the rivalry was when I actually lived in Utah. Now that I don't live in Utah anymore and you're not on the schedule, I really couldn't care less about your team.