You probably learned these lessons elsewhere, but I probably learned it earlier than you did and had it reinforced for 8 years (I started playing flag football when I was 8). The biggest lessons were teamwork and sacrifice. Football is unique in that it's the only sport in which all 11 players on the field have to all do their job at the same time or you lose. In every other sport, a single star or two can dominate the entire game and win for the entire team. In football, the quarterback gets his ass kicked if all 5 of his linemen don't block. A star linebacker can stop the run and short passes (if the defensive linemen do their job), but can't do anything for the sweep or long pass.

Football is also a good way to teach strategy. Unlike other sports where plays are limited due to the ongoing, chaotic nature of most sports, football stops after every play. You can sweep, pass, run up the middle, screen, option, etc. There are lots of options that may or may not work from one team to the next. You have to take a lot into account when coming up with a game plan, including the specific team you're playing. It's why coaches are so obsessive about going over game tapes. As my coach liked to point out, football is the only sport where you need an entire week to prepare between games.

And before everybody jumps on me about 'you can learn these lessons elsewhere/through video games', yes, they probably can. That doesn't negate the benefits kids get from playing football. I won't mention the health benefits you get because you get those from playing (just about) any sport.

Also, a funny anecdote, I only played 2 years of high school football before bailing. I played for 6 years for an independent organization called 'Pop Warner Football'. My coach for pop warner was an entrepreneur who owned and ran three concrete companies in three separate counties. He coached only because his son was playing. My high school coach had no idea what he was doing, which is why I didn't play my senior year.

If high school football got banned, I imagine Pop Warner will step in and pick up the slack, if they haven't already. Back when I stopped playing in the 90's, they had already expanded their program to compete with the Junior Varsity program. That's what I mean about football having too much support in the community. If the insurance premiums and lawsuits increase, they'll just have another bake sale.