The 407 is actually a pretty good example of government inefficiency when it comes to planning and building highways.

It exists because the 401 wasn't built with sufficient long-term capacity, even after it was widened significantly.

I wouldn't really consider the 407 a true "private" highway, though. It's more a case of the private sector rescuing the government from a typical government-created debacle, and last I heard, the highway is now majority-owned by the CPP Investment Board (a Crown corporation).

Have you ever actually driven on the 407, by any chance? It's a much nicer experience than the 401, although having to pay a toll while also paying significant taxes can be annoying. Under a proper system, there'd only be usage tolls, and no taxes involved.