Alright, lets imagine what you say.
I build a private interstate next to a public interstate.
Lets say it costs me $0.20 / mi per honda civic that travels on it, and the public road costs $0.30 / mi per honda civic that travels on it in amortized costs.
At the point of use, the user sees my toll of say, $.25 / mi with some profit, and at point of use the user sees $0.00 for the public highway.
Who on earth would bother to take my toll road, even though it is more efficient and cheaper? They've already paid the tax, and not only that, it is largely invisible to them. The government will literally imprison them or take their shit if they don't pay it, it is a sunk cost, the government has violently usurped my competition via payment under threat of violence.
You can't compete with 'free' at the point of use enforced by a violent actor against a sunk cost. Yes if you buy a plot of land that appears to not even be accessible by vehicle without some kind of unknown corner-crossing easement (one linked), then you will win out vs the non-existent competition there, but of course if the government shows up and taxes you to build a road even then you would lose.