Steve's barking; Building public works by reverse thinking

In today's world the public sector builds buildings, road and other forms of infrastructure  by competitive bidding. They take the lowest bid from firms that have a track record. Now for some reason the cost of what initially agreed to goes many times over budget. Now what would happen if we were to reverse this process by saying we have ex amount of money to spend on let's say a bus terminal. Oh let' s give it a number 1.5 billion dollars. Now any company that thinks they can make a profit building this bus terminal can had in a proposal that the appropriate age agency could decide the correct design, with the appropriate material and work rules.
It would then behove the private company to complete the job. The private company then assumes all the risks. It would be none of government's business how much profit. It would also compel the hired company to do them job as fast as possible to make a greater profit. Any bad decisions would be on the company, with the liability that goes with it.
Do I think there would be corruption. Probably, but there's corruption now.