I've had Uber drivers say not to bother using the app at LAX. They need to get a separate permit from airport officials to pick up the passenger, so it's at minimum a ~30 minute ordeal to arrange pick-up.
Uber isn't right for every use-case; especially pick-ups from regulated areas where taxi stands are already prevalent.
I always use Uber when arriving at SFO now. I know the pricing ahead of time (Uber does flat-rate between SF and SFO). I don't have to worry about having cash on me or getting a disapproving glare when I ask about using a credit card. I don't have to even think about calculating a tip. If my driver is rude or unsafe or anything negative, I have an easy avenue to report that without having to make a phone call, wait on hold for who knows how long, and then push my complaint into the black hole. If I'm especially tired and want to treat myself, I can order an Uber Black instead of an UberX. Hell, most UberX cars are nicer than most cabs I've seen.
The only downside is that there's a short wait if I don't time the ride request just right. Since there are tons of taxis at the airport, I wouldn't have to wait taking a taxi. But the above more than makes up for this point.
Uber has higher-quality cars and you get to rate the drivers so they tend to be a little more polite and professional. Not that taxis can't have high-quality cars and drivers but it's more of a crap shoot.
Well, the author's "palm-to-head moment" was going TO the airport. But even getting picked up at the airport can be a bit nicer in a town car. No line, no wondering if they take credit card, no dirty car, no tip, etc.
