I have some strong opinions on this.
First, I served as the administrative officer for a large youth football club in the DC area. We had five teams in various weight classes and about 100 kids. In the five years I did this, we had one serious injury in 200 games and hundreds of full contact practices. This is a "select" league and our "franchise" had dozens of kids who went on to play in college and even some that went to the NFL. . A kid dislocated his hip after being tackled on the part of the field that was baseball infield. The doctors said it ws a congenital weakness in the hip.
But kids were hurt. You wanna know when? The got hurt doing horseplay before and after practice and in their backyards. When they were supervised with equipment there were rarely injuries. Left on their own, there were plenty of injuries ... because they are boys.
Secondly, through the years, it seems to me that the parents who didn't let the kids play football and learn from the experience, produced boys that were less confident and more fearful. The parents let their own fears take over.
Football isn't for everybody. A wise man once told me that a football field was the greatest place in the world if you wanted to be there and the worst place in the world if you didn't. But don't let your --- or your wife's --- imagined fears deny a boy an opportunity to try it and find out if he likes it or not. There's no shame in not wanting to get knocked around if that isn't your thing. But at least have them try it. No pressure.