Typically there is a special tax assessment district when inside city limits - for example, my property in Georgia inside an HOA has a city millage of 0.003, but the streets of the community were indeed deeded to the city. On the other hand, if someone wants to build not actually inside city limits, of course they’ll need to pay for their own roads and utility maintenance since the county isn’t responsible for things like that.
Even if your HOA is not gated and doesn't have a clubhouse, not a pool, it is the HOA that is responsible for maintaining the streets and parks.
But... that is normally paid for by tax money. Yet the home owner's taxes in those communities are not lower. So the city is double dipping.