@tj Access to Admirals club is #1 thing. When I travel solo I'm often working in the airport and these are great places to work from. And food / drink included. Wife really likes having a standard, relatively quiet place with snacks to hang out when we're connecting.
Then:
4x American Airlines Miles on American purchases (1x Loyalty points - this is how you get status).
10x miles on aa.com/hotels and aa.com/cars (YMMV on whether booking via these are worth it for you, but you can get deals where you earn as much as 21x LP and 30x miles pretty easily from aa.com/hotels) (1x LP on the credit card spend)
1x everything else (1x LP)
Couple things you get with status, but if you have this card and somehow don't have status with American, complimentary checked bags and priority check-in, security, and boarding.
There is $120 credit on Avis or Budget car rentals annually
TSA Precheck / Global Entry credit - $100 every 4 years
$120 on lyft per year ($10 per month if you use 3 times and pay with this card)
$120 on grub hub per year (again $10 per month)
20K LP boost (10K each when you hit 50K LP and 90K LP) - LP don't have a ton of direct value, but gets you status, so having 20K less to go to whatever you're looking for is nice. Plus starting at 175K LP, there is some real value to be had from the milestone awards.
LP is how you get status at American airlines, and the credit card opens a path to earning a lot of LP. Status gets you complimentary domestic upgrades, and even-better lounge access if you get to at least Platinum Pro when you fly internationally. I personally value the miles at $0.02 each meaning I have enough faith I can get that when I redeem that I'll pay cash on a particular flight if I can't get that much or higher on a particular flight.
American status is fairly valuable - even only getting to Platinum Pro (2nd highest you can earn, 3rd highest if we count invitation-only Concierge Key) I've been upgraded on 50% of my flights. I think I can get to Executive Platinum for this year - and the credit card enables getting the 200K LP you need for that. Then at just Platinum you get complimentary Main Cabin Extra seats (which on American also come with complimentary booze in addition to the legroom & reserved bin space).
So there's direct benefits from the credit card, then the benefits of having status which otherwise would be hard for me to get or the ceiling would be significantly lower. That being said $595 annual fee - may or may not be worth it for any individual. American just hits well on where we're flying to/from and will be an even better airline for us if we do move to Charlotte.