Consider need for water treatment pipes run to and from each house for water and sewage as well as sewage treatment infrastructure.

Someone has never heard of "well and septic".

Out in the country, you have enough biological diversity around you that sewage is just fertilizer for your lawn. You don't need the extensive network of sewers to concentrate it, the chemicals to treat it, and the sufficiently large body of water necessary to dilute it back down to something that nature can tolerate.

Much the same with potable water: there's no need for an extensive system of water treatment plants, chlorination, the network of underground piping when you are just pulling water up out of the aquifer. It has been filtered through hundreds of feet of sand and gravel, in the absence of oxygen. All the biological material has been filtered out, leaving just water and some trace minerals.

Electrical infrastructure is moving away from centralized fossil fuel plants to distributed solar and wind power. Spreading the load out allows generation to be moved closer to the point of consumption, which reduces the total load at any point on the grid, and increases redundancy and resiliency.

Spreading homes apart introduces a natural firebreak between them, reducing the demand on fire services. A single kitchen fire in an apartment complex can put hundreds of people out of their homes. High-rise fires are especially dangerous. It's much easier to attack a house fire than an apartment fire.

Roads are not reduced: food and raw materials used by humanity come from the countryside. Transportation infrastructure must stretch out to the farms and mines. Housing farmers and miners in the cities just increases their commutes on top of their long work days.

Wireless data can be much more feasible in the country than the city. Less building interference; less RF interference.

No, I'm afraid you've overblown the cost difference considerably.