We know the methods exist because we've used some of them before: https://www.tradelineinc.com/reports/2007-10/unprecedented-t...
What we don't have is a political method to ensure the per-project technical incentives are correct.
* Information Asymmetries: I don't know anything about you or any other org working to combat this so I'm not comfortable spending money on you.
* Coordination Problems: Where do we act, on what scale, etc.
* Value Assignation Problems: How do I benefit from this for the effort I need to put in?
* Risk Problems: What is the chance of success solving a problem of this scale?
Essentially, I'm only seeking to explain. Personally, I have no problem with the system existing as it does. I would prefer other systems out of an inner desire for elegance. But I'm pretty proficient in acting within these to my own benefit so I won't tear it down. Perhaps part of the problem is getting folks like me to care to change this. I'm happy to cheer you on, though. Good luck!
That's the status quo. It sucks, therefore find a way to blow it up. Make it so that it doesn't work. Require the contractor to buy cost overrun insurance from an insurance company which obligates the insurance company to pay someone else to finish the entire job if the original contractor exceeds the budget by a penny, then let it be the insurance company's problem to figure out how to make the company come in on budget or contract the job out to someone else who can.
Once you blow up the bad thing (making construction projects exceed their budgets), the path of least resistance to more construction jobs becomes the good thing (many more construction projects that meet their budgets). But you have to blow up the bad thing first or it remains the status quo.