ehcwang,
The major U S. carriers now determine status based on dollars spent, not miles flown. (There are some exceptions for flights taken on partner carriers.) So I very much doubt that half a dozen cheap, Economy Class roundtrips between LAX and NYC would get you status on any of them. That said, depending on your non-airline spending patterns, you might well be able to achieve status on AA. AA instituted a new scheme (Loyalty Points) this year for achieving status. Dollars charged to a Barclays or Citi AA credit card earn Loyalty Points, as do hotel stays, car rentals, and spend via AAdvantage Dining, AAdvantage e-shopping, Simply Miles, etc. You can read details of the new Loyalty Points scheme here:
https://exploreamerican.com/newaadvantage/