From an accounting standpoint, gross money in be money out is what matters. Per capita makes sense to compare relative benefit, but realistically Montana is small potatoes on the Federal Balance sheet. Measuring per sq mile seems like some ludicrous ploy by Alaska’s senator to screw over New Jersey.

Or, the same data with a very hard to read circular bar graph visualization:

https://howmuch.net/articles/federal-budget-receipts-and-exp...

The numbers are actually pretty straightforward. "Expenditures is a broad category and covers a variety of things, including direct payments to people like Social Security, contracts for local governments, wages for federal workers and sub-contracting work."

Infrastructure costs are U shaped where extreme density is expensive, but so very low density. Mail delivery is a clear example where ultra low density just makes things more expensive.