I doubt AA loses any money on an award redemption unless they or a partner airline have massively screwed up their revenue management model and made seats available that they shouldn't have. The true cost to the airline of an award redemption is the marginal cost in fuel and catering of carrying an extra passenger. Meanwhile they booked the revenue for the miles redeemed months or years earlier. Payouts to partner airlines for award redemption are a tiny fraction of the ticket cost and again based on marginal cost.

Remember award availability is supposed to be distressed inventory that they predict will not sell. They make a ton of money off mileage sales (whether through CC or direct purchase) and it's unfathomable that this is hurting AA. It's like the only profitable part of their business.