Another potential pro of booking through BA is that in the event of needing original routing credit due to IRROPS etc, it’s easier when BA issues the ticket and is the marketing carrier for at least some of the flights on an all-AA metal itinerary.
I think the EC261 point is a fair one in general, and worth considering, but not relevant for the OP, since the itinerary appears to be all on AA metal regardless of who issues the ticket and/or markets the flights.
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