Airlines do compete on elite qualification levels. It is not that obvious with oneWorld (but even in oneWorld: BA used to have only 2 levels: Silver and Gold and all Silvers were automatically Sapphires with lounge access etc.). With Star Alliance you can get Star Gold by flying 20k miles (A3 - Aegean Airlines) or 100k miles (Miles & More) - benefits (on all airlines other than your own) are exactly the same. There was a thread on A3 forum, that they actually make more money on its FF schema than on flying. The tricks works because when you are an A3 FF flying on e.g. LH, this basically means LH has to 'purchase' the miles from A3 (IIRC there was a thread on BD forum about how it works, but 'purchase' is a pretty adequate word).
QR may decide to keep its qualification criteria to be more competitive for status seekers than AAdvantage.