Does it, though? Every driver I've talked to basically drives for "all of them". Several told me they try to find whatever apps are local for driving and they setup those alone with Uber and Lyft and simply take whatever pays the most / is more frequent.
Uber's software and network are solid but I don't think there is a whole lot of loyalty there. Anyone who can drive a wedge into a spot in their business could slowly erode it, IMO.
Now, they're too big to die quickly or anything like that. But it doesn't seem impossible at all to me.