I've been picked up by Uber several times at LAX with no problem.

I've been dropped off by Uber just once. That one time, the driver asked me to fill in a pre-order form to make it look like I pre-booked the ride, presumably to cover his ... if he was stopped. This was a very simple form, and I'm in a comfy car with a bottle of water, so it wasn't a hardship for me.

Funny story - my wife and I flew into Burbank and LAX a week apart and got the very same Uber driver! And then he picked us both up again in West Hollywood a few days later. Kind of spooky.

One LA Uber driver told us that new Uber guys are being assigned to Orange County as there is too much capacity in LA County.