Empirically denied.
If what you're saying is true, where are all the private intra-city public transportation services?
My warm fuzzy memories of Manila and other Philippine cities could serve as an example. The jeeps left over after WWII were used for decades after as microeconomic businesses. If you owned one and decked it out with cool stuff, people would flag you down, give you ten or twenty-five centavos and ride to the market . They were always packed. Some enterprising folks extended the wheelbase and could carry more. Competitive buses, ala our old school buses were packed too for some commutes. Over there, I was aware of little union deals where some collective sort of management system was allocating routes in some places, so it wasn't "perfect freedom", but it was very inexpensive.
I'm vaguely aware that government can be a good thing if some ideals are being incorporated in the way things are done. A city could just as well let out bids for transportation services, maybe for several competitive licenses and maintain some rules within their little kingdom, without having to be using sales tax revenue to support an inefficient city-operated system. . . .
I'm also vaguely aware of the eminent domain issues and sometimes necessities for building something like a metro trax line. I haven't got into advocating competitive water and power utilities exactly so I have to admit I'm not a real pure freedom advocate. I'm just thinking there might be a better way to do things in some cases that could result in better management/lower cost/more choice.
So I think your argument that these things don't pop out that way because public systems operated by government employees are just infallibly better than all other ideas has just not been allowed, by government officials, yet, in many places.
I do think even government officials desiring to promote use of their systems ought to quickly see the sense in Agoxlea's proposal, at least in some of the more central hub locations with higher traffic volumes.