Neither is road infrastructure basically anywhere in the world... Here in Australia we have a fuel tax and each state has registration fees but combined those don't even cover half of what is spent by Government and local councils maintaining existing roads and investing in new road infrastructure, and that's before even thinking of the hidden costs of traffic enforcement, ambulances responding to accidents, etc.

It's the same case for basically everywhere around the world, driving ends up being quite heavily subsidised too.

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?

True for local lines of everyday transportation. But actually high speed trains are sustainable, at least in France.

But also they are super expensive.

That's a bold assertion.

Never mind that you know what's also not "sustainable", if the definition means "costs > revenues"? Automobile roads :)