When Lyft launched here in NYC it was pretty dead, and they lost the initiative with the initial batch of riders. They've since rallied around driver recruiting and now the service is good. Everyone I know here has multiple ride hailing apps installed, and multiple services are competitive with Uber re: driver availability.
So yeah, it's not trivially easy to get into this game, but it's also not absurdly difficult - you need someone with deep pockets, but not that deep. This is especially true because Uber's network effect between markets is pretty minimal - people mostly take rides in their home market, so it's easy for upstarts to compete for a single market without the pressure to take themselves global immediately.
One structural weakness on Uber's part (and Lyft's, too) is that their commissions are still quite high (20-25%?) and this gives a lot of room for competition. Juno launched here successfully simply by undercutting the commission.
Additionally once Uber reached monopoly status and started raising prices, it would become more attractive to new entrants to enter the market. So even if Uber managed to beat all their competitors they still would have a price ceiling. All in all I think Uber provides a valuable service and can probably turn itself into a (very) profitable business, but I'm not convinced it will ever be the undisputed leader of all things transport that its current valuation seems to imply.
With the legal barriers in place, I was incredibly impressed with Austin's Ride Austin arrangement. Incentivizing drivers to keep more money in their pocket is going to be pretty damn compelling and unique legal environments encourage new entrants.
Uber has an incredible brand and has become the "google it" of ride sharing. That's very valuable and defensible but it risks becoming a colloquial "kleenex" for ride sharing.
The service will automatically hail from whichever service is the cheapest. Then pull an Amazon and expand into only the most profitable markets.
How many travel aggregator sites are there?
In comparison, a taxi ride might not even be the priciest purchase of the day.
All else being equal. A competitor boasting "hey, we're just like Uber, but with longer waits" probably won't get far. They could compete on
* lower price (fixed rate vs dynamic pricing, like Wingz)
* higher class of the vehicle
* support certain edge cases like kid-friendly service, bilingual service or women driver (hat tip Bojack Horseman Season 3 for that business idea)
There are more than 100 other countries out there with many cities in need of taxis.
As you point out, drivers and riders can install multiple apps (and they often do, e.g. Lyft), but for a competitor to enter they'll likely need to jumpstart their network. Something which they'll likely have to do by subsidizing both drivers and riders. This means that whoever decides to take on Uber would probably need quite a big war chest themselves.