There are states with ‘closed primaries’, where certain elections are only open to registered party voters - ie a Democrat would not be allowed to vote in the Republican primary and vice-versa.

This, and ‘because that’s how we’ve always done it’ are probably the main reasons party affiliation is part of voter registration.

If a party wants to hold a closed primary, can't they do that themselves without help from the government? Why would the government be involved in a party-internal election?

It always interests me how much of the US electoral system is just obviously completely broken from the perspective of outsiders, and it seems strange that people within the US see procedures like this and view them as normal and legitimate.

I'm curious what you see as "obviously completely broken" about the current primary process. Previously, party candidates were chosen via convention, which effectively left the selection process to party elites.

Deleted my previous comment as it didn't directly address your question. I don't know all the history behind it, but in terms of "can", I'm assuming that no, parties were unable to effectively hold a closed primary in a way that was well-run and accessible. And a poorly run primary vote defeats the purpose of having any primary in the first place. Using the state infrastructure and schedule makes the voting process much easier for the average voter, without being a burden to the state political parties.

As to "why" the government should feel obligated to subsidize the process -- because the government has the ostensible goal of facilitating fair and proper elections, and presumably the primary process -- which is not Constitutionally-enshrined -- is a net benefit to the general election, at least compared to selection-by-party-convention. In the future, political parties may decide that it's better to have open primaries, but that's orthogonal to the government providing the voting infrastructure and logistics.

Mostly for primary eligibility. It also allows for things like ensuring that poll watchers etc are available in a equitable way.

Why is the state getting involved in primaries? That should be the parties' business. I think there should be no public record of party affiliation.

Primaries aren't enshrined in the Constitution, but they became state business in the 1970s because there was a desire to let the average voter have more say in the selection process, which had previously been done via party conventions.

https://www.washingtonpost.com/news/monkey-cage/wp/2015/05/1...

I would prefer going back to party conventions instead of the endless campaigning :-)

Either way it boils down to $ spent to “win” the nomination. Whether it’s spent on advertising or back room wheeling n’ dealing it’s just money spent.

My (very uninformed) guess is that this is cultural. When democracy spread, Europe already had a good system of tracking people. The church was keeping records of every family for hundreds of years already. In contrast, the USA is a country of immigrants where new people without a history came in all the time. Tracking who votes where could not rely on an established system.

Voter registration is fine but why track party affiliation?