I think this is a very naive and somewhat wishful thinking writeup. You neglect a major reason why Rockefeller was able to obtain a monopoly: he controlled literally every part of the process of extracting oil, from the wells to the pipeline to the tank cars, in an industry that had high startup costs/barriers to entry.

You basically look at every way in which Uber is doing a great job and then declare they will have a monopoly. It's not like they are the first successful business that is killing it and you don't have any truly remarkable arguments for why no one else can go do EXACTLY what they are doing. They have a head start: big whoop, so has any great company.

For Uber to obtain Standard Oil style monopoly they'd have to do something very different that you don't mention: buy a good portion of the cabs and cars and black car services in the world. In the end those cars are the actual supply, and Uber DOES NOT OWN ONE CAR. Do you know how many of those companies exist? Do you think that 1) Uber is even interested in acquiring them and 2) that'd even be possible if they did? Do you think that every single one of them would come onto one platform and that Uber could convince them to be that one platform? You don't think that in certain regions or countries other companies, the Lyfts and Sidecars and Hailos of the world, won't make a move and lock down certain markets first and become the defacto option in those cities?

You also neglect the fact that in many cities (downtown new york?) getting a cab is super easy. In some cities there aren't enough uber cabs going around at any one time to have an on demand app work necessarily, and for other trips private transportation in the way Uber offers might be exorbitantly expensive (getting to certain airports, etc.). You neglect the fact that they are targeting one behavior, a massive one, but still one behavior: the on demand ride. Lots of people like to plan their rides in advance.

Overall this reads like it was written by a fanboy, little real analysis of why, despite the fact that Uber is an awesome company that is doing extremely well, they have any real chance of having a monopoly.

It is a transportation planning and booking app. Orbitz, Expedia, Kayak, Hipmunk, you name it are all in the transportation planning space (but for flying) and everyone has their preferences etc. There is room for more than just Uber and the idea that they will just take over everyone is ridiculous.