JDiver

So, here's the deal, to the best of my knowledge.

Positive Passenger Bag Match is a requirement when one is departing internationally. It is not a domestic (US50) requirement (unless it's in the airline's AOSSP, which is restricted from being viewed by passengers etc.). Once one's checked bags have been cleared by the TSA, they can go on different flights than the passenger they belong to. The difference is that in most cases the airline can choose whether to separate passengers and their baggage, whereas they might permit - or deny - a passenger's request to be separated from their baggage - but usually in cases of IROPS / OSO.

So it's still essentially an airline employee's choice, not a passenger's preference in this instance.

AA Conditions of Carriage state: "General acceptance of baggage
Only baggage as defined in the definition section will be accepted for transportation. All baggage is subject to inspection. Checked baggage will be accepted for transportation only on flights on which you are traveling. American will not accept baggage whose size, weight, or character makes it unsuitable for transportation on the aircraft as determined by American." (An agent could further interpret this to mean on your booked flights, unless they have reason to route baggage otherwise.)

However, airlines prefer to not do what the OP wants for another reason as well. What's that? Because most passengers whose bags aren't at the carousel will go fill out a missing bag report if they don't find them immediately. This report, once filed with the airline, becomes part of the FAA published late or missing bag statistics.