When the Council has paid parking, then paying for parking on their aerodrome is fair, IMHO. But not if they have no paid parking in their LGA - because they are being selective in who they charge. Why charge aircraft ("to maintain the airport and cover the budget to do so" in your words) when the road budget for most Council's is significantly higher than the aerodrome budget? When you go to the Council swimming pool, do you pay for parking in the pool carpark - or do you just pay an entry fee for the pool?
Would it not make more sense to have toll roads and paid parking to offset the expenses incurred in maintaining the Council road network? Of course. But most regional Council's don't. Why? Because they know full well it'd be political suicide to introduce paid parking at Temora, or Narromine, or Scone - but those rich pilots who dare fly in? They're fair game at most airports.
It's a very Australian thing but governments in this country seem to hate aviation and I have never really understood why. Whether that is a full blown conspiracy or just the nature of bureaucracy I don't know. Most likely the latter however it is everywhere. It is almost like governments in this country do not want any aviation activity to exist at all. Roads and railways are the only "approved" form of transport and they will subsidise those inefficient forms of transport forever regardless of cost, be it environmental or monetary.