The upgrade is technically done so through a price reduction rather than an on arrival thing. E.g. if you reserve a full size, you're paying the midsize rate. That being said, especially as an elite, you usually can ask for something nicer. If arrived early enough to LAX or when it's not too busy, usually asking if there are any upgrades available to EE results in something. Just make sure the gate people know it's free. I've had some issues in the past of accidental charges