There don't have to be toll booths. If you think that's a bad idea, why assume it would have to be used?
Another option is a monthly subscription fee for unlimited access to all roads a company owns. If there are a small number of large companies this might be convenient. And don't complain about fear of monopoly -- the alternative is a total government monopoly.
There are various possible ways the road use for subscribers only might be enforced. Offhand, none sound especially convenient. But they all sound better than the status quo: all people in the area are counted as "subscribers", even if they don't own a car, and are all billed, and this is backed up with guns. That's worse than any of the non-ideal enforcement mechanisms I can imagine. And while it may save a bit on transaction costs, it does that by not even trying to differentiate a subscriber from a non-subscriber.
How do you collect the money if there are no toll booths? Subsidize the private corporation by having police stop people without them?
You don't seem to be considering a couple of things:
The "backed up by guns" (if you want to have a serious discussion, these sorts of libertarian cliches could perhaps be checked at the door) tax funded roads have benefits that extend beyond the road users. "Externalities" as it were, in terms of lower prices for goods that are easily and quickly shipped to the area, competition for other modes of transportation, and perhaps jobs in sectors like tourism.
If, ignoring the externalities, you wish to more directly attach the costs to the people utilizing the roads, you could raise gas taxes. Of course, that has its own positive and negative aspects, and winners and losers.
The real world is tremendously complicated, and I don't think it's really possible to predict everything. However, I don't think that means that you can simply ignore some of the more interesting facets of economics and say "errr, just let the market take care of it" - it's just too simplistic.
Another option is a monthly subscription fee for unlimited access to all roads a company owns. If there are a small number of large companies this might be convenient. And don't complain about fear of monopoly -- the alternative is a total government monopoly.
There are various possible ways the road use for subscribers only might be enforced. Offhand, none sound especially convenient. But they all sound better than the status quo: all people in the area are counted as "subscribers", even if they don't own a car, and are all billed, and this is backed up with guns. That's worse than any of the non-ideal enforcement mechanisms I can imagine. And while it may save a bit on transaction costs, it does that by not even trying to differentiate a subscriber from a non-subscriber.