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.