One or Woster's commenters, John2, suggests the following:
If you want SD and the US to have 1st world secondary scholastic achievement results then take a modern model from nations that do: Denmark, the nations of northern Europe, Japan, South Korea, Singapore, Shanghai, etc. Focus on scholarship. Put all extracurriculars where they belong – in clubs outside of school jurisdiction. These leaders in secondary education excellence took the US model and improved it with up to 230 , or more full contact days per year. The US, on the other hand, is frozen in the 1950’s Happy Days-era of high school games and year books.Both Cory and John2 have an important point; schools should focus on academic content. It's irresponsible for a high school principal to suggest that a gym is as important as a science lab or library. That's not to say that a gym is unimportant, but it doesn't rank as high as a library or computer lab.
Further, I would not object to a longer school year as long as it had breaks dispersed throughout it. I've long advocated a school year that followed a 6 weeks on and 2 or 3 weeks off pattern.
That being said, a longer school year or eliminating non-academic extra curriculars won't change much of anything. The club sports that spring up will dominate students' priorities because they are "fun." Parents will probably put a higher priority on club athletic events than they do on current extra curriculars because they are paying for them. Further, if club sports become the norm, schools will probably lose funding because clubs will want money to build gyms and practice facilities. In the court of public opinion, bread and circuses beat math and literature every time.
I wish I lived in a world dominated by Cory's and John2's thinking. I don't. Given the thinking that dominates American culture, the educational and activity framework South Dakota has now is probably the best we can hope for.