Citation needed.

Public transport in larger cities is generally profitable as the seats are well-filled. Commercial companies pay the government for the privilege of being allowed to operate the services.

Public transport is indeed not very profitable in rural areas, as you're running a bunch of mostly-empty buses in order to provide the bare minimum of usable connectivity. The companies operating them are paid by the government to do so.

Besides, it is myopic to look solely at ticket prices. Roads are incredibly unprofitable as their maintenance costs far exceed the tiny amount of money brought in by vehicle taxes and fuel duties. But we're okay with that because the added value to the economy more than compensates for that! Lose money on road building, make money by taxing the companies who drive the trucks sustaining their businesses over them. Why not take the same approach with public transport?