Competition is possible, it just is rarely worth it. NYC subways worked fairly well as a competitive system until the city started passing maximum price laws (which in turn meant they couldn't maintain the system and eventually the city took it over). However the competition meant redundant service to the dense areas as each built there, at the expense of less dense areas that should have got service. It also meant that where lines did cross each other (a complex task even in 3d) they generally didn't built transfers even though a single system would have.

The claim competition is not possible is therefor false. We can debate if we want it, but it is incorrect to claim it cannot work.