I suspect they have a way to mandate how local governments handle the voting. The US does not. That's the barrier.
Yes, it does.
It does for federal legislative elections because while the Constitution gives power to run those elections to the State in the first instance, it also gives Congress the power to jump in and regulate anything it wants about "the times, places and manner of holding elections for Senators and Representatives, [...] except as to the places of choosing Senators".
And, while it doesn't have truly mandatory federal direction for Presidential elections (for which voting by the people isn't even Constitutionally required), it does in practice for them the same way much of what is done in Presidential elections is already fixed: safe harbor laws defining what states must do to protect their electoral votes from being subject to challenge when counted by Congress.
The US chooses not to exercise the tools it has to mandate how local government handles the voting, and where it does exercise those tools doesn't do it well, and that's the problem, not the absence of the tools.
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.
