Yes, I think the generous interpretation is that it isn't the sidewalk, but perhaps the sewage, water, electricity, comms, and maybe garbage collection that become expensive in less dense areas. All stuff that is related to the sidewalk, but not actually the sidewalk.

No, this is a matter of different strokes for different folks. Many people have chosen to live in low density areas even though there are no sidewalks. They have chosen for themselves what to do with their limited resources. For people who choose to live in cities because there are sidewalks there, they are the ones making the tradeoff that you like.