JetBlue has already figured this out (sort of), minus the status accumulator, by allowing you to create a family pool, and having the miles you earn from flying be deposited into the pool. This is why now when I'm traveling with my family on AA, I'm crediting my own flight to AA, but everyone else's to B6 so I can pool all of the points. True, it doesn't do anything for status, but it does give me redeemable miles/points in one account. And Marriott allows you to transfer points between family members for free (plus you can earn points for more than one room if you're paying for it, as was mentioned above for Hyatt and Hilton).

There are multiple ways this could be enhanced if AA wanted to.