it is unclear to me whether US CBP ever requires a notarized consent letter at the time of a child's departure from the US. Do they?
No. Travelers leaving the US generally do not come into direct contact with CBP. Instead, for those leaving by air, airlines pass their information to CBP. If there were a requirement for departing travelers to show such documents, it would be noted on airline websites. You should certainly check specifically with your airline, of course.
Do airlines ever request it (even if the destination country does not require it)?
I can't say for certain that no airline has ever asked for such a document when the destination country didn't require it, but I can say that airlines typically stick very closely to the requirements of the destination country. That has certainly been my experience with vaccination requirements (both for yellow fever and COVID-19).
Also consider that many single parents travel with their children. If permission of the second parent were routinely required, then you would see airlines requiring single parents to prove that there is no second parent, but this sort of thing is not in evidence on airline websites.
The title mentions TSA. TSA does not concern itself with requirements for travelers to cross borders.
While these documents are not required, it can't hurt to have them. They are inexpensive to produce; many banks will notarize documents free of charge. If someone does decide to check whether there is another parent who permits the travel, the document is very likely to satisfy them more quickly than would otherwise be possible.