Parents are funny about their kids and sports. Even in laid-back California, you hear about parents who push their children to be better and better, to outshine everyone else on the field. Other parents are just happy their kids are running around outside and having fun.
There are probably as many reasons parents allow or encourage their children to play sports as there are parents. If they agree on anything, it would be that the children be safe, that no one be carried off the football field on a stretcher, that no player is knocked unconscious.
Sports carry a certain amount of risk with them, though. A scrape or cut or the occasional minor sprain may not be something to cheer about, but it is tolerated. This is what happens in sports.