These companies would have to buy the land from the government or from people who own the land, like everyone else. If you say that the government gets it with imminent domain and that sucks, well, that's another topic, isn't it? Since that's what it currently does. We're only discussing selling the roads to private owners that the government currently owns.
If we don’t have a monopoly in charge of a large chunk of land, turning right will cost you an extra $10 as opposed to going straight. For that matter going straight more than 5 miles may cost you an extra $10.
This is already the case, if you miss your turn you might be on your way to a toll bridge since you missed the last exit and there's no way to turn around. Of course, you would be using an app that can either optimize for driving time OR cost. This is also the case now as you can go around a toll bridge, but you'd have to go all the way around the bay to save a few dollars. This isn't something new or materially different
If they don’t place this regulation, people that live at one end of a private road and work at the other will be required to pay extortionist prices
you can stop using a road that's too expensive and take a bus from a road that is cheaper, the land owner will be forced to decrease the prices until people stop avoiding it
In the end of the day, it seems to me that people will pay more to drive, and the government will still have such a high level of control of the road system that any benefit that could be found in privatization is lost.
This isn't necessarily a bad thing if it causes cheaper public transport options to become available.
Overall, I don't know if it would be better, I'm just saying it's not as ridiculous as people might think.