I think OP is generalizing when he writes whether AA pulls a plane out of a hangar when the original plane goes down for maintenance. From my experience, the answer is yes - but generalizing that AA will switch aircraft where there is an available aircraft that can replace the original aircraft.

#1 DCA-MIA: flight computers would not talk to each other. AA 737-MAX switched to a regular 737-800.

#2 LAX-DFW: passenger lost cell phone down vacuum toilet on AKL-LAX 787 inbound. MX determined there was not an easy fix so we swapped out that aircraft for a different 787.