Saying that infants or children should be banned from flights or premium cabins because they sometimes cry is just as ridiculous as saying that adults should be banned because some of them get drunk and shouty from time to time. I’m sure most parents would be trying everything they can to calm a crying infant down. Why would you not?
My kids have both flown with us from a few weeks old and are definitely better behaved than most adults in premium cabins.
If it was me in the OP’s situation I’d put my headphones on or a set of earplugs and not get worked up about it. It’s public transport after all, and they’re not breaking any rules, as the airline has rightly pointed out.