'Four in ten (79%) British adults, including a majority of those with young kids, think it would be a 'good idea' for airlines to reserve areas for passengers aged 12 and up. Only 13% think the move would be a bad idea.'More here http://yougov.co.uk/news/2013/08/27/four-five-want-child-free-zone-planes/
Of course it's a popular idea, flying is bad enough without having a screaming baby assaulting your eardrums. Flying is uncomfortable enough without having a five year old kicking the back of your seat for 4 hours. Flying is nasty enough without having the baby in the row behind you throw up over his parents and you. Flying is nauseating enough without you having to witness someone changing their baby's nappy on the other side of the aisle.
All of the above examples have happened to me over the last few years...
What I don't understand is why airlines that operate multiple cabins on long haul flights don't designate one cabin in each class as child free. I'd pay a 10% surcharge to be sure of a relatively peaceful flight.