I've asked a lot of people without kids, if they did have kids, would they stop kayaking? I think I personally would, because I like kayaking hard stuff and that is the most likely to get you. It seems like most people I ask would do the same. There are a few badass kayakers out there that have kids and run the gnar...but I have also heard one say he is terrified of his kids liking kayaking and wanting to boat what he boats.
Kayaking is fucking dangerous, but also really fun. Safety in most groups is an afterthought. When things go bad in kayaking, it happens fast. Sometimes things look like they are going to hell and they turn out ok. That is why so many of us, in my opinion, keep paddling hard water after a near miss. Your mindset changes about how dangerous kayaking is if you nearly watch your good friend die. Kayak long enough on hard enough water, and you will see that too.
The health insurance topic seems well covered in this thread. My 2 cents are everyone should have health insurance. The moment between not needing shoulder surgery and needing it in kayaking, is typically a second...at least it was for the person I watched tear their rotator cuff. Head trauma is generally instant. Thank goodness I've never seen that, but I do have friends who have had helmets shatter on them going off drops, flipping part way down and hitting their head on a rock.
All this said, I have been kayaking 12 years injury free. Knock on wood.