The thing is, babies cry, and sometimes there's little that can be done to stop them crying. But that doesn't meet there isn't something to be done to stop everyone in the surrounding area suffering from it.
The solution I propose is a sound-proof baby care cubicle. The cubicle would be large enough for an adult to sit with the baby, and would also have a cot area. The cubicle would have a built-in baby monitor (as well as some of the features of the previously discussed baby pod).
Such cubicles would allow one care-giver to look after the baby (and suffer the noise) without nearby people suffering the consequences of the noise (including other children that might be woken up).
The cubicles could be used in maternity wards, and could be rented to new parents.
An extreme version of the cubicle would have a sound-proof vestibule that would allow entry and exist of the cubicle without any of the baby's noise being released into the environment.