The whole point of charging for the parking spot would be so that they wouldn't have to use tax money to maintain it.
It's not a matter of alleviating your tax burden, it's a matter of alleviating everyone else's tax burden so they're not subsidizing your car. You should pay for what you use unless there's a compelling reason for it to be subsidized, not the other way around. Roads are essential for freedom of movement and in any case are too difficult to toll on a massive scale, so it makes sense to subsidize them. Parking spaces are inessential and easy to charge for, so we should charge for them.