I have girls, so haven't had to deal with this issue. My older daughter plays in the high school band, we're around football, and I don't judge the parents who let their kids play.
But would I let mine play? Hellllllll no. I'd be the bad guy who said "nope, you're not doing it, deal with it" no problem.
Pick a different sport. The science is irrefutable, the risks are huge, and there's not jack shit being done to actually minimize them, because the truth is you can't without radically changing the game, which no one is willing to do. Too much money involved, too many people who think they're invincible, who find it easy to ignore the problems because they're slow to manifest.
I dunno though, I see comments like this:
Quoted from MotorCityMatt:If you son plays hard he will be fine, it's when you don't play hard that's when you get hurt.
and I don't mean to single anyone out, it's just an easy example, but that's nonsensical. Playing hard is exactly the problem. We're not talking about broken bones or fucked up knees here, we're talking about your brain. There's no fix for it. High school football is the number one source of sport concussions, look it up, this isn't something you can hand wave away with "oh, he's not in the NFL".
It's your kid, and it sounds like you're pretty aware of what's really going on, but there's living life to the fullest, and there's making smart choices to have a good life to live. My two cents, since you asked, I wouldn't presume to tell any parent something like this unprompted.