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If you want to call something a monopoly, you can do so. You could make an arguement that every store has a geographic natural monopoly in the area immediately surrounding. It doesn't change the fact that they must compete.
There is competition with roads. Multiple roads do lead to the same areas. There's the "last mile" thing that you get with ISPs at present, but there are a great number of roads you can take from Miami to New York, or New York to Buffalo, or Boston to LA.
Not all monopolies have high prices. Competition exists on many levels, including dollar competition, where everyone has to compete against absolutely everyone else for the customer's dollar.
In areas where road owners abused their "monopoly", people would just move out and stop using the roads, and go to places where the roads are inexpensive.
Tolling isn't the only potential system for private roads. There's subscription-based roads, where you buy a license and get a plan for road use, as you do with cellphones. You could just transfer ownership of the road to the adjacent landowner, and the landowners would discuss road maintenance . You could do it a number of other ways. If tolling is inconvenient, another system will be devised.
I agree that the poor should be exempt from gas and property taxes. So should the middle and upper classes. After all, the upper classes just pass the cost onto the lower classes.
That you can make a rebuttal does not mean you automatically win.