lrickets,

Maybe you're thinking of some other airline? AA most definitely does have a 50% discount (off any domestic fare AFAIK) for infants under two flying in their own seat.

You're right that parents also have the option of having infants fly for free on their laps (or of course on any adjacent empty seat), but to my mind the 50% fare is money well-spent if there is any chance of a full flight. Infants are much safer (and I think usually happier) in their own car seat.