At least on an accounting basis though, airlines do actually make remarkable profits on their frequent flyer programs. In 2015 or so United disclosed their FFP business was earning ~67% margins, as against ~2% for the rest of the airline. I don't think they have disclosed more recent numbers, but margins are probably higher now.

That said, these profits are in part an accounting artifact. This is because up until very recently airline accounting rules only required carriers to realize the marginal cost of carrying a passenger when frequent flyer miles were redeemed. Since the marginal cost of a passenger is only ~$20 or so, this yields great margins.

These days however the overwhelming majority of airline miles are awarded for credit card spending rather than actually flying, though. As your second article notes, for United the split is 70/30 or so.