If you look way back to my trip report last December to WDW, I grappled with the same issues.
My kids, 2 and 4 at the time, are not the calmest to begin with. The first flight for both was a lot to take on.
In deciding about first class/not first class, my thoughts were:
1) they would not appreciate it
2) my wife and I would be busy entertaining them, and we would not appreciate it
3) I would not want to be subjected to kids like mine if I was in first class.
4) I can deal with coach on a 2.5 hr flight.
As it turned out, they were fine, and slept through most of the flights. (My youngest woke up 15 minutes before landing on the trip home, didn't understand what was going on in his ears, and cried the whole way. Crying, like yawning, opens cloged ears, so I held him but didn't try to stop him.)
Once they are older, and understand that they needed to behave differently, I would not hesitate to book them in FC. Just like they can eat fries off the table in McDonalds, but have to use a fork at a fancy restaurant, they would be taught the manners required of the situation.
But, kids are kids. And with the headphones and the drone of the engines, you probably can't hear much anyway, so lighten-up.