I've been in a lot of Karate schools, mostly in New England, Californian, Hawaii and Florida, but in other places as well. I've been in more dojos that do allow contact to the head as opposed to those that do not. Control is the key. Heck, even in boxing gyms, nobody is trying to kill each other, or knock each other out. There are exceptions, sure, but they are just that, exceptions.
I think the reason some schools do not allow head contact is that's the way they were originally taught by somebody else. And I think part of it goes to the old joke, "How many Karate teachers does it take to change a light bulb?"
Answer - "Change? You want to change something? Nooooo!"
I'm actually horrified when I read about broken cheekbones requiring surgery that came from dojo sparring. I don't even know what to say to that. For forty years we had head contact in sparring, but never had anything remotely close to something like that. Black eyes, sure, some broken noses, cracked ribs, but fighting is a contact sport. To me, the KEY is teaching people control. And control isn't some mamby pamby way of hitting lightly. Proper control teaches how to hit as lightly or as heavily as you want, as your current level of skill allows.
My kids classes always had head contact. And there weren't any injuries to speak of. And, yes, their parents were there watching. We were always very careful with kids. I'm sure everyone here is, too. When one of the kids got a bloody nose we would all rush over and excitedly say "what color is it, what color is it?!?! They'd look and say "red?" We'd all cheer, address the bleeding and tell them "red is good. If it ever comes out chartreuse or orange that's not good." This, of course, would usually lead to them asking "What's chartreuse?"
To which we'd reply, "That's your homework for tonight, next class you tell us what it is." And in the course of about twenty seconds the kid really didn't care about blood coming out of their nose. Or ever again for that matter. If it happened again, they'd say, "It's red, coach, I'm good!" And the parents? They loved it.
We allowed groin contact as well. The way we looked at it was, if you were going to be throwing head kicks, you damn well better know how to protect your groin while you were doing it. Wearing a cup under your uniform was mandatory in every single class. If you didn't want to do that, that was okay too, just train some place else, no worries.
Heck, back in the day the majority of point tournaments we went to allowed groin contact as scoring a point.
To us, throwing a punch to the head and pulling it before it connected was the equivalent of learning to shoot a gun and purposely missing the target.
And to reiterate, the injuries in our school were far lower than other schools. Especially the ones that didn't allow head contact. I believe the reason for that was in those schools head and face contact was accidental. It's very difficult to control accidents.