Uber's service is more than just an app. They have operations teams in every market they operate in to onboard drivers, deal with local issues, etc.
Think of it from a driver perspective; if a competitor pays less than Uber and has less demand, why drive with them?
And if you think there will be a competitor capable of out-spending Uber using venture capital, think of it from the perspective of a VC; why pour so much capital into a business so unlikely to succeed against an incumbent when you could put it into the incumbent itself?
I think the primary risk to Uber's business is that of a self-driving competitor being capable of disrupting them; such competitors will have capital already, and will be capable of disruption through all the same ingredients that got Uber to where they are. Those companies would probably work with Uber at least at first, anyway. Uber will be at their mercy every time the contract needs to be renewed.
Uber had to spend money to test the waters and figure things out. Competitors can just copy.
I think they will probably end up working with the first company to have autonomous cars "ready". The big question is what happens next. Will Uber be at the mercy of that supplier every few years as the contact comes up for renewal, or will autonomous cars become so commodity that there will be multiple players competing to be Uber's supplier? Another possibility is an M&A event.
Some companies just have a much bigger ramp up than others. Amazon has so many markets to build warehousing & logistics in. Uber has so many markets to establish drivers in.
The subsidising of rides makes complete sense; subsidised rides are loss-leaders aimed towards building habits. I haven't seen their data, but it seems like a good plan.