I don’t travel enough on airlines that have Frequent Flyer programs to have “status” on any airline and I’ve found it beneficial to have both American Airlines and Qantas FF memberships.
Two ways this has been helpful.
1. Sometimes radically different points needed for exact same award flights.
For example, American Airlines from any Australian or New Zealand destination to any US destination (e.g. Sydney to New York), one way is
37,500 American Airlines points
Using Qantas points Sydney to New York one way
64,000 Qantas points! That’s 170% of the points AA requires.
For these flights the actual flights taken are the exact same flights – as in the same aircraft.
2. Points earning opportunities differ.
I’ve found that certain flights operated by OneWorld alliance airlines don’t earn the usual 1 point per mile Qantas points but do earn the full one point per mile American Airlines points.
I mainly bother with Qantas points because I have a credit card that earns Qantas points and not being from the US I’m not able to get a credit card that earns American Airlines points.