How the airlines can get back in black

I know next to nothing about the inner workings of the airline business. Strike that - I know nothing about it at all. But something occurred to me yesterday during my flight home from Newark to Chicago, when I was treated to not one, not two, not three or four, but FIVE screaming babies. And they were well-oxygenated babies, too - they screamed from take-off to landing. Two full hours, and I'm not kidding.

My idea is this: if all of the major carriers offered one or two flights a day on their most common routes as child-free, and charged those who wished to buy tickets on those flights some percentage more than the normal price, it is my carefully considered opinion that they'd make a fucking fortune. I know I'd pony up, the woman I was sitting next to thought my idea was brilliant, and so did some friends in chat last night.

So, obviously, I'm missing something fairly big about why the airlines haven't jumped all over this. Is it illegal? It's not like they'd be denying people with babies the opportunity to fly...