I think your explanation is satisfying. I just wonder why the federal structure of the nation can't mitigate this difficulty, but i know that there are basically empty states especially in the central part of the US so the low population density made everything more difficult

Yea, but for example, in italy we know basically exactly how many people can vote in an election because our Ministry of the Interior takes count of every single citizen with an active electoral card skimmed from the deaths (Every death must be reported to the health authorities), to avoid fraund

Yea, i read, but this "approximately" let me uncertain, maybe thanks to language barrier

Sorry but, just a question, you don't have a clear number of potential voters in US?