A political party is free to change the rules for nominating candidates however and whenever it chooses. It is free to nullify the decision of those voting in a particular primary. A political party is free to nominate whomever it chooses [and almost certainly multiple candidates for the same office it wishes should it choose].
Ultimately the party, not a judge, chooses whose vote matters and whose doesn't. Placing the imprimatur of the state upon a political party's process doesn't change that or make the process of candidate nomination little 'd' democratic. The people within a political party charged with making the rules for candidate selection are not elected or selected little 'd' democratically. The process of nominating candidates is not little 'd' democratic in any meaningful sense.
This is something we should take away from them. The outcomes of private party activities shouldn't have any impact on the names that appear on ballots. They can maybe mark the names they choose to endorse as an organization, but we should throw away the system where the parties are directly involved in putting names on the ballot (of course they'd be indirectly involved, as an organized group is, uh, organized and thus more ready to act together, so would have an easy time dealing with ballot petitions).
I think the barriers to entry should likely remain high, but we need an overhaul of the voting system itself to break the two-party system, which itself is just a side-effect of the mechanics of our voting process, not anything mandated.
If I remember correctly, early on in the country's history the founders noticed that the mechanics of voting were trending towards a limited two-party system, and that consternated them. Most every (if not actually every) democracy established after the USA has a voting style and representative bodies that allows more parties to coexist, or creative destruction within the set of active parties to thrive.
I'd rather have some system of arbitrarily limiting the number of names on the ballot than a system that privileges parties. For instance, for statewide elections you could choose the 5 (or 10!) names that had satisfied the ballot requirements in the most voting districts (so it doesn't matter that Uncle Larry likes to "run" for state senate in his home county, he doesn't kick someone with a better/actual shot at winning off).
It turns out that satisfying the ballot requirements is already a challenge requiring organization, and that organization is called a political party.
The public has a vested interest in having a ballot present only those candidates who can demonstrate a minimum-level of popular support. Otherwise why have a qualification process at all -- we can give voters phonebooks to take with them into the booth, and they can find the name of whichever citizen they feel should be elected.