The infrastructure isn't paid for when it's built (including the public house). It's financed on debt. Pay-by-use is just a form of tax payment.
It's just that the "use" for information is nearly free, so it doesn't make sense to charge for usage.
If the road was already completely paid for by tax-payers (no debt), and then a toll company wanted to operate the road for a 99% margin - you'd see a lot more people complaining about that.
Street parking is an interesting example in that the demand charge is probably unrelated to the underlying cost. However, it's just one of the many examples of taking tax dollars from Pot A to pay for things in Pot B.