There's another important thing you aren't thinking of: just because a lot of studio execs work in Burbank doesn't mean they live there. In fact, I'm guessing very few of them do. Places like Santa Monica, Pacific Palisades, Brentwood, and Bel Air are are as convenient to LAX as BUR, if not more so. Add to that the better amenities at LAX (FL for those paying for first to NY, AC for those forking over for business), and a lot of extra options if one flight (the one flight with the OP's proposal) is delayed or cancelled and you have a strong case for keeping AA's resources largely concentrated at LAX.