Whether an item is taxable has nothing to do with one's carry-on allowance. The space OH and underseat is limited and thus this is a zero-sum game. With the exception of certain carefully excepted items, the limit is two items of specified dimensions.

The fact that duty free is sometimes distributed after the gate reader is a matter of logistics, not AA rule.

Bottom line, for every person bringing a third carry-on with them, there is someone who must gate check something (presuming full flights and the like).