One problem with a private road system is that roads take up space and prevent people from using that space for something else. I think that property tax on road surface area would be prohibitively expensive if a private entity were to own it.
Another problem is that building or expanding a road through an already populated area basically requires eminent domain.
We should never privatize profits deriving from public investment.
What happens when a company buys both routes between town A and town B? What free market forces are going to drive down prices?
According to wikipedia, for each dollar collected by the 407, $0.21 goes to maintenance, and $0.79 to profits ($0.66 are paid out in dividends). The 407 collects $1.3 billion dollars annually with double-digit annual growth.
Private roads are economically unsustainable and serve only to leech wealth from society.
The iPhone revolutionized mobile phones and greatly expanded the interconnectivity of the world. And yet nobody is demanding that the general public should subsidize Apple.
The only way Amtrak gets to raise rates is if it drastically improves service.