They would not know where to begin. All road construction is contracted out by a publicly opened competitive bid process. The contracts never pay that great but you know that you will get paid in a timely fashion (as per the contract pay period). Governments bid out so many contracts that they know exactly what the going rates are for each unit price bid. When a contract is advertised (as by law it must be) there is and accompanying engineer's estimate. The engineering is now generally bid out too. If the prices come in higher than 10% above the estimate usually all the bids are thrown out and it is re-bid. Bidding government work is not gravy work. But at least they are an owner that is experienced.
Some governments still do some minor road maintenance. But less and less. They know they can save money bidding work out.
I think most governments do an okay job in their role. And most of the money is collected from gas tax. I think it is fair. I do not think the transportation infrastructure would change much if it were in private hands.