Ouch! Unfortunately been there done that with our son...3 times! Forget the ages now (he's 17 now), maybe 8 the first time...then a year to the day later he did it again! Made it past that date the next year, but like 6 months later he did it again! All his left arm...elbow twice and wrist once. Was really getting nervous that DCYF was gonna start asking questions.
Ouch. 3 times...
Just some food for thought, but even at younger ages, having kids start on any grappling style is potentially beneficial in a multitude of ways. Aside from the obvious benefits for self-defense, one of the big ones is that styles that emphasize grappling and/or throwing all have a lot of focus on developing kinesthetic awareness of body positioning AND break falls (how to properly fall/land to minimize the risk of injury).
Simply as an anecdotal example, my brother and I both started formal martial arts with karate (I began earlier, despite my brother being 2 years older), but I also developed an interest in all the aspects of martial arts, including grappling and throwing.
My brother broke his arm and dislocated it multiple times from falls (not to mention getting stitches on his head on 3 different occasions from falls not related to any extreme sports).
In my case, learning HOW to fall/roll and distribute the force of a fall saved me from injury many times, and despite being more of a nut in my youth (doing stuff my brother didn't, like a LOT of biking in all kinds of terrain/conditions, skateboarding etc., and even eventually going from point sparring to full contact kickboxing), I managed to avoid any broken bones, aside from finger injuries (which ALL occurred while playing basketball. Lol).
I was present more than a few times when my brother was injured simply from tripping or slipping. The same type of falls I generally didn't even have a bruise/sprain from due to instinctively falling as I'd trained, to minimize the force of the fall and any chance of injury.