Part of the difference, I think, is the odd importance of the state in politics and governance. States came before parties existed. The founding fathers not only didn’t expect parties to form, they loathed the concept. However, the realities of politics engendered two factions to form into parties within only a couple of years after Washington became the first president.
But the basic power unit remained the state. State legislators directly elected (or appointed) senators. It wasn’t until the 20th century that the general public got to vote on them. The House of Representatives represented local constituents in segments of the states. (Rotten boroughs, as in British politics, were deliberately made impossible.) Delegates to the Electoral College were elected by states to stand for a candidate, rather than voting for the candidate himself.
And then there were all the elections internal to the state. The governor and Lt. governor. In some states, all sorts of additional offices are voted on. Attorney General. Commissioner of Railroads. Comptroller. State judgeships may be voted on, which is unusual elsewhere. These offices, especially the judgeships, were not necessarily sorted by party membership. In some states all judges must run as independents.
So the state regulating all election proceedings was a natural outcome of the unusual federal/state split in the U.S. government.
And the split of the country into slave and non-slave states exacerbated this. Even before the Civil War, almost all political power in the slave states was concentrated in the Democratic Party. It certainly was for a century afterward. These were effectively one-party systems, with the barest token existence for Republicans. In all these states, the real election was the Democratic primary. Whoever won that won the office at the regular election, because there would be either no or only token opposition.
It gets weirder. All states are divided into counties, and county governments in most (but not all) states are powers of their own. Cities and towns and villages are separate entities, even when their boundaries co-exist with the county boundaries. There are dozens of offices in county and town governments, and all of these fall under the state election laws, and all or almost all of these also require primaries. And then there are multitudes of school districts, all of which are internal to counties or cities but separate in most ways from the other governments. And then there are a zillion special voting districts for fire protection or whatnot.
Again, all of these have to be overseen by the state government. Each state sets a state voting day, normally in November. This day, under current laws, is also the day for federal elections, which occur every two years. All candidates have to be registered with the state and properly approved in all ways under all regulations sufficiently far ahead of time to print up the statewide ballots (which also may include any number of propositions, state constitutional amendments, and other non-positional votes).
So the only way to eliminate chaos, and lower the incredible costs of an election, is to have the state oversee the party primaries as well. These are also done on a single day for statewide races, and other races often piggyback on top of these. (Localities can have separate primaries and even elections for strictly local races.)
All this is a major reason for the mechanical and electronic ballots we have. I know that posters from other countries made incredulous noises at the outcome, or rather lack of, in the 2000 presidential election. Why not just count the X’s, they asked? It’s because a ballot may have literally dozens of simultaneous races on it, with candidates from a dozen or more political parties (who may run on more than one line in some states), at a half a dozen levels of government, hardly any two of which are co-terminus in area boundaries. It’s amazing we get elections counted on the same day on any regular basis.
But the woolly history of U.S. political divisions and the history of parties and their politics are so intertwined in the U.S. that there is no hope of separating them. Especially since the party that controls the state government gets to write the laws under which the divisions operate and the elections are held. It’s a horribly bad system in many ways, and a wide-open small-d democratic system in others, but it’s uniquely ours.
And so complicated that outsiders can’t be expected to understand how any of it works or how the whole comes together. I assure you that most citizens don’t.