Do you want to be able to get on any American flight even if it's sold out?
Most of the benefits from having a specific airline credit card or earning miles come in the form of free or discounted services such as priority boarding, checked luggage, lounge access, or upgrades.
The most valuable benefits are the ones that cannot be purchased. Those are rare and usually require achieving a specific status with an airline that is earned by taking many flights each year.
Guaranteed availability in main cabin with 200,000 loyalty points
The American Executive Platinum status which requires earning 200,000 loyalty points in a year gives you and a companion guaranteed availability in the main cabin. You'll have to buy a full fare economy ticket, which can be expensive, but being able to get on a sold-out flight is a huge perk for anyone who flies frequently. It trumps any standby priority perk.
As long as you book at least 24 hours in advance of the flight departure time, you can book any American flight, even on the busiest holidays.
How can American offer this? Either they hold some seats back from general availability, or you will be upgraded to business or first class if there are open seats in other cabins, or the airline will have to pay to bump someone else off the plane.
How to achieve American Executive Platinum status
Airline rewards and status systems are always complicated to understand, but compared to other airlines, American loyalty points are pretty straightforward. A loyalty point is the same as a bonus mile without factoring in bonus multipliers. So if you earn 2x miles on your American credit card for purchasing American flights, $1 counts as 2 bonus miles, but only 1 loyalty point aka base mile. You earn loyalty points from flying on American or using your American credit card.
If you spend $200,000 per year on an American credit card, you will have this perk for the following year. American counts points earned from March 1-March 1 instead of a simple January-December calendar year. The American Executive Platinum status has many other perks such as free checked luggage, free extra legroom seats, priority upgrades, priority standby, free same-day flight changes, etc. But these are based on availability, so there's no guarantee.
American has the most straightforward status program and you can achieve that status solely from credit card spend. Other airlines require significant flight activity to reach special status and no other airlines offer guaranteed main cabin seats.