I think that the OP was more asking if AA and/or UA didn't have FFP, then lower fares would be the direct result.
I agree with that, ant it's not because people are choosing higher airfares when lower ones are available.
In the end the airline knows that the miles will be redeemed for free tickets so they tack on $20 - $40 per itin to recoup that loss. Not only that but administrative costs and all that junk. If UA didn't have to offer a FF program it would make their fares cheaper.