Others objected to coaches setting the rules for the more than 7.6 million students who played high school sports last year and scores more who played on club or private-league teams.
At least 34 student athletes died that year, the alliance said.
"In most states, the state high school athletic associations control all the health and safety policies for our student athletes," said Douglas Casa, an expert on sudden deaths in sports and a professor at the University of Connecticut who helped write the proposed rules. "That should scare a lot of people in this room. If you had a family member with cancer, would you seek out a coach for advice? Their opinion on health and safety issues is not relevant."
Some 400,000 concussions occurred in high school sports during the 2008-09 school year. More than 7.5 million students played that year, the National Federation of State High School Associations reported.
Thirty-nine student athletes died in 2011 and 49 in 2010.
The decline is in part because 43 states have passed laws that require a doctor's note before an athlete returns to play after a concussion injury.
But while the total number of injuries has fallen, the rate of concussions has risen, leading to long-term health risks for these athletes.
"Think about this: You get an injury in the NFL, you have two guys at your side right away," said Christopher Nowinski, the co-director of the Center for the Study of Traumatic Encephalopathy at Boston University's School of Medicine.
That is seldom the case in high school fields, where more students die than in college or professional competitions.
"We do not provide a single professional medical person to half of high schools," the former Harvard football player and WWE professional wrestler added.
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