This may be true, but if those experts would have only been paid if the project came in under budget this surely would not have happened. Incentives matter more than expertise.
"You only get paid if the project comes in under budget" might just only give you the lower-tier players who have no better project to work on -- maybe the more professional people would say 'no way' to an arrangement like that, especially given the % of these projects that wind up running over.
Then you wind up over budget with a sub-par contractor in charge of the project.. what do you do, change horses mid-bay? No way, turns out the threat doesn't even have teeth.
After a constant stream of cost overruns the US military tried to do fixed price contracts for awhile. What happens is the big players don't bid, or they do it through independent subsidiaries.
Then when the project costs balloon the contractor comes to you and says "Look, you have two choices - either you can modify the contract so we can make money, or we'll declare bankruptcy and you'll have to write off every nickel you've spent so far."