I suspect that it will make sense for some Hyatt and American elite members to focus just on earning Hyatt status, transfer some Chase points to Hyatt and redeem for AAdvantage status for each trip you wind up making on American – and just travel on whichever airline makes sense on a given trip.
If you’d just be an occasional American traveler this may make more sense than striving for AAdvantage status – especially if you’re doing it now with spending on an AAdvantage credit card. Earn more and more valuable points (like Chase points) spending on a different card instead, and redeeming ad hoc whenever you need the status.