Many people have already done the math many, many times, and it always works out to be a lot cheaper to have dense urban areas.
I just moved from a dense urban area to a rural area. Taking everything into account - yes, really - things are unambiguously cheaper here. That’s a common result in the US. If you want to blame a single thing, I’d go with lack of housing supply in cities due to exclusionary zoning, but I hit some other weird figures like municipal water+sewer being more expensive than a well and septic system (again, yes, taking everything into account including construction costs).