Any parent who would allow their kid to compete without being cleared from a concussion is an idiot.
My son's high school baseball coach didn't allow any participation in any other sport once tryouts started. Due to a two day snow storm delaying the town basketball rec league championship my son had to sit on the bench and watch his team lose a championship game they would have won had he played. The coach stated the rule every year in the September baseball meeting. The rule didn't apply to fall ball. He was ticked he lost a starter to a broken ankle in a rec basketball game when my son was in 8th grade.
Our state laws do not allow participation in the next season's sport until the previous season is finished. Tyrelle Pryor (Raiders) once scored 27 points with 16 rebounds four games into the season because he had to finish the state football playoffs before playing basketball.
We had two athletes who had waivers from the state to compete on the Junior US Teams and US Teams simultaneously with the same and other high school sports.
My son's soccer coach cringed at the idea he was playing fall baseball. There was a big talent dropoff to the backup goalie. The high school basketball coach allowed his jv players to play in the town rec league. I once asked him about his players get hacked by aggressive, less agile football players.
My son was a very talented skateboarder and snowboarder. He gave up competitive skateboarding for safety reasons in high school.