There are a few kinds of private roads
-public access private easements (my road)
-public access non easement (grocery store parking lot, cost amortized by customers)
-toll road (some highways, etc)
-completely private road (only owner uses it, i.e. private farm road)
Only the first of those has the potential for the kind of abuse you mention, I think, because it mimics the government kind of road in some ways where the maintenance costs aren't captured at the point of use. If it gets bad enough charging $0 you might need switch to some other kind of private road.
In any case this isn't nearly as bad as the tragedy of the commons situation if it is a government road, I think, at least as implemented. Our county roads have a tragedy of the commons situation where you could use the road and then some totally unrelated grandma gets dragged out of her house for not paying for it, despite the fact she's never even been on the road -- to me that seems strictly worse "tragedy of the commons" than even the public access private easement because at least under the private easement I can't initiated violence on unrelated persons for other people using the road.
It would seem quite hypocritical (and ironic) indeed to me for proponents of public roads to damn private roads under the idea of tragedy of the commons, so I'm not sure it's a valid indictment here that the tragedy of the commons is somehow becoming even more unsolved when roads are privatized.
That's not what I was asking. The definition - at least my def - is different, your cases don't explain how to solve it - indeed, there is no known solution, and that's the point. You can't get around government, which can solve some problems.
The only "known" solution is to privatize the commons. One way to do that in this example is to use a toll road.
It seems bizarre to damn some methods of private roads for not solving something you claim has no solution, then just glance over the ones that mitigate it.
You've shown no reason why you can't "get around government" but rather just dismiss the ways that just did.