What might still move uber from a fluent market into a winner takes all position some day would be a shift to their own fleet, either driverless or with employees. That would then be real investment and as such would be much harder to match by a newcomer than the day to day underselling they are currently doing to artificially to balloon themselves up.
And there are other factors. If a competing service let me choose what model of car turns up (say among nearby ones), I may pick that. After all, a big advantage of these over owning a car is that you can try different models.
I don't think the winner takes all, any more than restaurants are winner take all though in theory restaurants also benefit from higher utilisation, less food wastage, negotiating power over suppliers, etc, as the number of patrons increases. That hasn't led to there being only one restaurant in each neighborhood.
However, I think uber pool/lyft line require a much higher critical mass of users to be effective than the basic lyft/uber services and there may not be enough users to fund more than one of those in some (many?) metro areas.
Also, just as cabs did, über will erect regulatory barriers to entry for smaller players.