Public transportation fails because of monopolies. Government-run systems lack the incentive to innovate, leading to decay and inadequate service for users.
Discussion
You obviously never travelled in Switzerland?
No, it fails because it is public. If the junkies didn't use it it'd be much better. Oh and also look at Switzerland.
When it fails a system lacks responsibility. Projects can be run by government, while giving responsibility to specific people. So when the project exceeds budget, the responsible person should pay the bill for it the same way the person gets pride and financial success when finished in budget.
This is rather a question of functional vs dysfunctional systems. Which is independent from government run or private run projects. Since in the end it is people who run the project anyways. The incentives matter. Who is the issuer of the incentives does not matter.
Where I come from (Valparaiso, Chile), public transport (Las micros) is completely deregulated and it's a mess, mafias are formed around it, drivers do extra hours and they are constantly racing because "the money is in the street".
People are desperately try to get the govt involved and add regulation.