Natural barriers to entry? Nope, all you need is a half-way decent mobile app and some people with cars. Yes, the bigger your fleet the larger an area you can cover, but there's no need to serve an entire metropolitan area if covering just some of it is enough to turn a profit. (For example, if I were going to enter the ride-for-hire market in NYC today, I'd put all my drivers at JFK, Laguardia, and Times Square.)
Artificial barriers to entry? There used to be, in the form of TLC monopolies and regulations around medallions. The nice thing about Uber's success, though, is that they're bearing the brunt of breaking down these barriers, leaving the path open for those that will follow.
Network effects? Mmm...some, but only for those that travel frequently. That is, if you often find yourself in a new city, your first act might be to open the Uber app because you can count on them providing service in a new, unfamiliar local. I'd wager that's the minority of ride-for-hire customers, though. Each city has its own local mass transit, and there hasn't been a push to standardize across regions. (Though wouldn't it be nice if your Metro Card worked on BART?)
On the flip-side, I see a lot of opportunity for new competitors to differentiate themselves. For example, let's say you decide to focus on the "regular customer": someone who travels roughly the same route most days of the week, a commuter or someone with a daily or semi-weekly appointment to keep. Imagine you could tune your service to get the same driver for these customers most days. Now you have a familiar face picking you up, who knows where you're going, what route you prefer, what station you like on the radio, etc. If I was that customer, I'd take that service over Uber in a heart-beat.
So, again, why should it be winner-takes-all?