I didn't know my biological father until I was an adult, so I never knew his father. But one day when I was catching him up on the activities my sons were involved in, he told me that he really admired how we keep them active and having fun. He said that HIS father did not allow him to play anything, not even basketball, on a team because he was scared of injuries. I had never heard of such a thing before! He said that while he sees that his father was trying to protect him, now as an adult and childhood long, long gone, he sometimes feels sad about how he missed out on a lot of fun. I do NOT want my children to miss out on their youth. I absolutely want them to look back at their childhood with smiles and lots of stories to tell! You can protect your children by providing them with properly fitting equipment, by teaching them the proper ways to do certain things (a properly fitting helmet when skateboarding or biking, holding the bat correctly, pivoting your back foot correctly, throwing in a way that won't make you lose your shoulder by the time you're 20, when playing soccer you MUST tackle with your leg slightly bent, etc, etc, etc). Teaching them, and getting them good coaches, will not only provide quality time in the backyard together, but also protect them while they're out having a good time. Any kind of hockey in my opinion could be pretty "dangerous", but your guys got hurt on a playground, not the dangerous sport. Funny how that happens. :)
I'm all for teaching them how to behave, how to think as they do things, to be aware of the world around them, how to do things correctly, and then let them play as hard as they want to play with those guidelines in place. There's a few situations where we may say no (my oldest is going to be too little for football, but we can steer him to all kinds of other options)....and my husband insists that while rugby has no pads, there are not the life threatening injuries that football has because the hits and positioning are different, so youngest may be allowed rugby, but husband says NO to football. I'm also picky about schools, classes, and coaches. If my youngest (bigger body type) pursues wrestling or some form of boxing, obviously I would shop for a coach that would do it in a way I'd agree with. My oldest is in kung fu and loves it, and while his teacher gets on my nerves sometimes, he's VERY good at discipline, respect, and when performing certain moves, he makes sure the kids know to do it very slowly and to obey a tap immediately (the consequences for not obeying immediately or hurting a classmate would be "dire", lol). For sparring, there's so much padding, it's actually kind of stupid looking. Little tiny michelin men on the mat.
But no, I've never met anyone personally that kept their child from being a kid just for fear of injuries (except my dad's story).....at least, noone that admitted it publicly.