Being based in Orlando, I am exposed to out of control children and their parents that simply refuse to take any corrective action, on nearly every flight.

I have seen many parents put on headphones and completely ignore their children's tantrums.

I have seen many Flight Attendants ignore the above.

Ultimately parents must control their children when they are in confined, public places.

Being a Father and Grandfather that has traveled with my own from infancy, it is easy to manage your children (most of the time) with a little bit of preparation.
Bring drinks, food, toys/games, etc. Talk to your children. When that doesn't work, Over The Counter Motion Sickness medicines will help them sleep.

That said, the FAA is failing the flying public by allowing "lap" children. This is a major safety issue.
When severe turbulence is encountered or their is an "emergency" landing, lap children become projectiles, can become severely injured or die, and can injure other passengers.

Finally, does a passenger in Business or First Class who has potentially paid upwards of $10,000 for their seat in order to enjoy a comfortable, peaceful, and quiet flight have the right to be free from screaming and kicking lap children who are essentially flying for free? Absolutely.