I have never seen AA charge a passenger to move to the exit row or MCE.
However, completely different on UA. UA FA's know who is sitting in E+, and if a passenger moves up to E+ then they get asked to make the payment for the upgrade. If they don't want to pay - they have to move back.
I suspect that UA sells more E+ seats than AA does MCE. Of course UA offers more E+ seats then AA has MCE, including international configurations. The legacy US aircraft in AA fleet really don't have MCE - only bulkhead and exit row.