I think there is a distinction to be made between infants that are crying as a natural response to a new/unfamiliar environment, not to mention the air-pressure changes, sounds, smells, etc. that can start a crying fit..... and the tantrums of a child who is of enough age to know the "proper" behavior of being in public who proceeds to throw a fit or behave poorly without parental intervention.
I was on LAX-LHR in biz in January and had a mom who purchased a seat for her 3-ish year old (they were seated in the middle 2 seats together, not a lap child situation), were directly across from me. Kid had the initial jitters of being on a plane which mom tried her best to quell, but eventually just gave up. Everytime the mom would put the child in the seat and then sat down herself, the kid wound up the lungs and was screaming. Not crying like an infant, screaming and being obnoxious. Not long after that, the kid ran rampant in the cabin. I saw it as a safety issue first, common courtesy issue second. I was surprised that the FA's didn't speak with her as we hit some serious chop over the midwest that made even myself blush and take a stiffer sip of my drink. By the end of the flight, side eye shade was thrown from almost everyone in a 5 seat vicinity of the epicenter.
Now, as much as I wanted to read her the riot act, I just kept my headphones on and figured that the karmatic gods would be just and serve down some be-fitting punishment for the lack of common courtesy to her fellow passengers. And realistically, the last thing I wanted to do was get in a verbal altercation with a mother defending the (inappropriate) behavior of her toddler at 35k feet - that would not have played out well in today's "fact's be damned" world of reporting airline related news.
Is there a good solution? Maybe a properly trained FA could handle it, but in today's prevalent "victim mentality" society, most of us fear the backlash of a situation going pear shaped and our good intentions suddenly being under a microscope.
But, I am pleased to know that for every parent who doesn't care about this type of thing, there are plenty of parents that do care and take responsibility for their kids and their behavior on an airplane. Hell, I have done the walky-bouncy down the aisle for a mom and child on a flight so she could have a break and eat dinner. It is a team effort up there!