I suspect they have a way to mandate how local governments handle the voting. The US does not. That's the barrier.
There's nothing magic about holding election, that prevents Florida from doing it trustworthily and would permit the USA do achieve the same feat. A great many states do it, some federal. It requires coordination and reliability, in much the same way as delivering the mail, supplying everyone with fresh milk, handling vaccines, etc.
Those "rights" (there's a problem with applying that term to states and not people, but its a side issue here) do not include the "right" to run federal elections without oversight by Congress, which has both direct and explicit regulatory power for federal legislative elections under the Constitution, and the Constitutional role of assessing whether electoral votes are properly given when counting them, and has, in fact, has acted based on the latter power to direct states as to what they must do in federal Presidential elections to shield their votes from potential challenge.
Some German states even partly devolve elections further. There was a minor scandal regarding that last year, when one city chose to deploy some software that broke (and as a result, some votes weren't tallied until many hours later than expected, perhaps >24h). That's the kind of scandal federally devolved elections can have, the kind the Americans should aspire to having.
