Simply put, it is more important. When applying for a job across the country, the prominence of your school's sports team matter more than the quality of the education you received. The person screening resumes in HR or sitting across from you in an interview, would be more encouraged to see a UC engineering degree compared to Rose Holman. They wouldn't likely know who Rose Holman is, and would simply screen them out early in the process. Unfortunately this is case, but it is reality.
"Doing both" doesn't answer the question and isn't reality in college sports. Which program would you rather have representing your school, Harvard's or Kentucky?
Yes I want UC to win a National Title with 4.0 GPA students. But if I have to choose between a National Title with 2.0 GPA students, or having a team that loses in the first round with 4.0 GPA students; you know which team you want. You also know which team the President of the university would want. Everyone is taking the title, and the benefits that come with it. It is what would be best for the university overall.