I don't know why the Government doesn't adopt the Tom Sharpe method of paying for mega projects like HS2. (Read "Blott on the Landscape")
i.e. We will pay you XX Billion for you to build the project. If you get the project completed on time we will pay you XX Billion. If you get the project done earlier then we will add a bonus of Y million. If the project is delayed then we will charge you Z million. I'm sure the tax payers would appreciate this as a way of reducing all the overspend and budget mis-handling, and maybe there would be a lot more support for a project like HS2. I think I'm like many others in the country who are getting tired of what is happening on the project, seeing taxpayers money being wasted on a project many of them will never use and even more will never get to see completed at the rate it's going.
Imagine you are one of the tiny number of infrastructure consortiums in a position to bid for, win, and construct a £100bn project. Bearing in mind that the Government can't ring up Dave's Building & Roofing in Hounslow to expect him to give a figure.
If the government told you, "please bid for this and also note that if inflation, costs, wars in Ukraine, pandemics, or other matters occur we are expecting
you to bear the whole cost of the extra expense
and pay us a penalty". But also tell you "if you do it cheaper than your bid, you'll get a bonus."
Keeping that in mind, what do you think your bid for the project would be? What you think it would actually cost? What you think it would cost, plus 10%? Plus 30%? Double the cost? More?
Noting that governments - even in arms length projects - have a habit of changing and respeccing and rescoping projects along the way, do you bid on the basis that you select the cheapest options and argue with the government if they want something different? Or do you bid on the basis that you'll buy 30 tunnel boring machines, clad every station in 18K gold, and manufacture the rails using depleted uranium, and let the government pay you off for contract changes to reduce the price at a later stage?
I'm sure you can guess the answer. Sometimes even that doesn't work. Ever heard of a company called Carillion PLC?
Generally even the government aren't stupid enough to try to enter into that sort of contract. Generally. (although remember the "cap and collar" franchise agreements that were a brilliant strategy to do pretty much what you suggested, but under which the DfT got royally screwed?)
Instead, the government would prefer what are known as DBFO contracts, where the consortium finances and builds it themselves (so they themselves lose the money if the contractors overcharge), and then charge an agreed fee for usage once complete.