Thread transferred to the BAEC forum, where this topic is well understood.

It's true that two award seats in the same class of service must be available to redeem the voucher, and if you intend to book a round-trip there must also be two award seats in the same class for the return flight. It's also true that substantial fuel surcharges, taxes and other fees apply, rendering these unattractive for economy class redemptions. It does appear that AA and BA have swapped a substantial amount of their transatlantic award inventory, creating the circumstance where AA offers award seats on BA flights when BAEC shows none (and vice-versa). This is related to fuel surcharges.

Nonetheless, we have successfully redeemed these coupons each year since they were added to the Chase card. It's challenging, but they are not worthless.