[alistairSH]

I'm not sure that's correct for primaries.

Primary elections are by party, so are by definition more extreme than general elections. A candidate must win over an average Democrat OR and average Republican, not an average across all voters.

Further compounding the problem, many states/districts hold closed primaries and/or caucuses, which limits participation to those with a strong interest in elections (either enough interest to join a party and/or enough interest to give up half a day or more of time to join a caucus).

[maxerickson]

Yes, private organizations shouldn't have special methods for placing names on ballots, the rules should be the same for everyone.

Groups can still endorse candidates in that world, it just doesn't impact the names that show up on the ballot.