Imagine if most of the high schools in the district did not have a football team, or if elementary schools did not have softball teams or Field Day. Few people would stand for that, and for good reason. But just as all schools should encourage physical excellence, they should encourage academic excellence, as well.
Academic excellence does not mean getting a perfect score on a test in class, just like physical excellence does not mean doing 20 push ups in PE, although both are great. Academic excellence means reaching beyond the classroom and testing ourselves against others. This isn't just for a few superstar students; there needs to be a team to support them, just like the star quarterback needs a team to support him and a team to compete against.
I believe the district should require/pressure/encourage schools to create math clubs, robotics clubs, chess clubs, creative writing clubs, language clubs, etc. to a much larger extent than they currently do. I understand that not all schools will be able to have every possible club, but to have few or none should be unacceptable.
The district could provide mentors for teachers or parents who are unsure how to run such clubs, and could provide small stipends that build over time until such "positions" are filled. To really be pursuing academic excellence, clubs should be encouraged to attend regional competitions and events to measure themselves against their peers from other schools and districts.