Its part of the "loveliness" of the electoral college.
In conception, the idea was that each state operates similarly to the member nations of your EU-- each state was supposed to have broad sweeping autonomy, with the fed level having minimalistic powers governing international politics, interstate commerce disputes, and wartime operations.
Everything else was supposed to be at the state level. The congress and senate are representative gatherings, intended to represent the interests of those autonomous states where such interstate commerce resolutions and pals were to be decided.
With this in mind, each state was, theoretically, its own microcosm of political authority, and the "republican party" in one state was independent of the "republican party" of another state. "Iowa republicans" and "california republicans" were presumably very different bodies, with very different goals, because they are in very different places.
Remember, the system was created in a time BEFORE mass transit and near-instant communication.
If it helps you guys from Europe out-- Imagine your citizenship no longer being "german", or "french", but instead now being "European Unionist", as the autonomy of those nations crumbles in the face of that of the council. (I think that's right--- the one that ISN'T elected.)
You now no longer have a "pirate party of germany", you have a "pirate party of the european union". Etc, and have people in belgum deciding what people in italy can and can't do.
The united states was not intended to be federalized to the extent that it is now. The requirements in the different states for primary elections is an artifact of the time before.