I have a 2 1/2 year old son, and my wife is due with a little girl in a month, so I have plenty of time before sports come into play. That being said, my wife and I have talked, and we are not going to steer him/her away from anything they wants to do, including football. Look, I am worried about injuries, but injuries can happen at any point in time. When I played football, I broke knuckles, sprained ankles, tore a groin muscle, hyper extended an elbow etc. My older brother broke a collar bone. My younger brother played up through college ball and was a QB; he actually broke his back, tore a knee up etc. That all sounds horrible, yes, but I can list injuries suffered from family and friends that DID NOT play football, but rather ran track, played baseball/softball, soccer, and some that didn't play a sport and those injuries would sound similar.
The fact is, injuries happen whether we like them or not. When your kids learn to ride a bike, they will probably fall. When rough housing around, someone may bang their head on the ground or on a table. You could trip and fall, braking bones when the sidewalk is uneven. The way I see it, we don't live in a bubble where nothing can go wrong. If my son and daughter want to play football, soccer, fencing, study karate etc., I will support them vs. telling them no out of a fear of the unknown. However, I won't judge someone that does choose to say no, as it is not my choice/place.