I don't really believe that you can show a direct correlation between physical activity and academic performance. But even if you can, I suggest that "more focused academics" would be a far more reliable method of improving academic performance than adding "physical activity."
As far as school being a place to "prepare students for life," I agree that school does that to some extent, just because because some subjects (economics, biology, math, reading) develop necessary life skills. If you are talking about developing socialization, well, kids don't need a gigantic sports program to socialize; they just need to be around other kids, and they would be around lots of other kids in their classes and daily routine. If you are talking about socialization coming from nonacademic pursuits, such as sports, scouting or cotillion, then those things should be done outside of school, and the public ought not have to pay for it.
Lastly, to your question about whether high school should be "solely for academics," I say "yes." That is, after all, the historic function of an educational institution. Unfortunately, school has become a kind of specialized day-care program for the masses. Day-care is important. But it should be paid for by parents; not the general public. And academics should not be watered down to carry out this function.