This is a grossly over simplified assumption that does not stand on its own. The type of monopoly that Google has was not handed to it, but resulted from "nasty" competition. Google (currently) is literally too competent to beat in the search engine space. Perhaps Lyft will die off or by purchased by Uber, but it's not a given that it should, or even that it will.
More importantly, what happens when there is no competition between companies for drivers? Are we assuming that once (Uber|Lyft) has the market wrapped up they're going to benevolently maintain favorable driver pay rates? Are we really assuming that in the absence of incentives to do so that (Uber|Lyft) will favor drivers or riders instead of its own bottom line? Since this flies in the face of common sense and a mountain of empirical evidence to the contrary, why in this case is a monopoly preferred to competition?