Part of the reason for the 8 class periods is to allow students the opportunity to take all the elective classes (like band, art, chorus, industrial arts, home ec etc.) they want and to allow them to be able to have a study hall so they can use the library or school computers if needed to do their homework.
Your scenario assumes that kids have no study hall/class time to do work and get 1/2 an hour of homework in every class every night - which is not realistic since their classes would include non-homework classes like gym, art, shop etc. and teachers who give that amount of homework would have to spend a significant amount of their time correcting it.
I agree sports (and other extracurriculars) are important - but not so important that time needs to be taken out of the school day for them. Plenty of time for competition and practice after the academic school day is done and students would also be receiving the benefits of exercise during gym. Typically the kids who would benefit the most from regular exercise are not participating in extracurricular sports.
A half hour is an average. Certain classes would have more, I don't remember teachers ever consulting each other as to the work load they were giving their students. Even when asked for a reprieve due to another teacher already assigning a large home work assignment, the answer was pretty much "not my problem". Every teacher feels that their individual subject is the most important and will rarely, if ever, give into that.
If you're allowing for a gym period then why can't the football, baseball, basketball, swim, track/field, soccer, or whatever else teams be allowed to practice instead of participating in dodge ball? I'd love to see you sell that at any school in the country. In addition you get back to coaches pushing for leniency of homework for students who practice after school.
It might work in your head, but generally in the south academics is very much second to athletics. For example, despite a manhunt for an armed fugitive the SWHS Seahawks continued on with their exhibition game.