It absolutely takes tremendous capital expenditure to build the network. Uber has an accumulated deficit of $20 billion precisely because they subsidized both drivers and riders to build the two-sided network.
It doesn't have to be winner-take-all. A duopoly in most medium to large cities is perfectly viable. But you won't see dozens of competitors because the drivers and riders would wait too long for a match in a sparse network.
Unless the ride-share commodity can be differentiated some other way, it would take large subsidies for a long time to make much of a dent in Uber.