Also, some airports have pre-flight inspections. That means immigration control is provided before boarding the flight. In that case US officials provide immigration control, and airline does not make any immigration checks.
As far as I remember, flights from Canada, Ireland and Aruba have pre-flight inspections. So, baby transportation letter will not be needed in cases like that.
Airlines of arrival are required by US law to send anybody whose admission to US is denied because of inconsistent documents, home for free. Baby transportation letter releases airlines from this requirement, even if the admission for the baby is denied.