Keep in mind that America is famously horrible at doing public projects of this sort cost-effectively (e.g. the NYC 2nd ave subway is roughly four times more expensive per mile than similar projects in other countries, including very expensive countries like Japan). There are various reasons for this, but a lot of it seems to be dysfunctional bidding rules etc. that result in few bids and poor methods for choosing the winner.
Other countries manage to do similar projects for vastly lower costs, and it seems pretty likely that an intelligently run private project in the U.S. could also manage to do a good job of keeping costs down. [It's not just labor costs, etc either—total cost per mile is remarkably similar all over the world, both in cheap countries and expensive ones, except in the U.S.]
Other countries manage to do similar projects for vastly lower costs, and it seems pretty likely that an intelligently run private project in the U.S. could also manage to do a good job of keeping costs down. [It's not just labor costs, etc either—total cost per mile is remarkably similar all over the world, both in cheap countries and expensive ones, except in the U.S.]