Indeed, you would need carrot and stick. The point the witness made was that under the current system you could not profit without collusion. (Edit to add: and that means that all honest people end up driven out of the construction industry). At least under a Vickrey system an honest person can make a profit hypothetically proportional to the social benefit provided.

The flip side is you would have to tell people that while you're going to increase what you pay them your tolerance for collusion (and it is essentially tolerated today) will go down, and mean it.