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.