I proposed what you are proposing and other questions. I had them turn it in on a piece of paper so there would be no pressure to answer how they really feel and after we would have no discussion about the topic. Fyi, three of the votes are from European exchange students. Here were my questions.
1. Do high school sports enhance or degrade the over all value to your education in high school?
Enhance 43 Degrade 0
2. Would you be in favor of no school sponsored sports?
Yes 0 No 43
3. Would you be in favor of no school sponsored sports but have sponsored intramurals?
Yes 0 NO 43
4. Do school sponsored sports help the over all culture of the school?
Yes 43 NO
5. Would you be in favor of all sports have zero cuts so everyone can participate?
Yes 2 NO 41
It's clear to me most students do not want what you are proposing.