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.
Whenever people talk about alternative voting systems, the consensus seems to be that it would be impossible to implement in the US. But why? What drives this obsession with choosing between two evils rather than choosing among several, where one's own views might stand a better chance?
But with regard to your question, the obvious explanation is that the voting method itself acts as a game theory attractor for a certain number of "viable" candidates, until a Nash equilibrium is reached. First-past-the-post thus eventually results in an entrenched two-party system.
This alone is ample reason for those two parties to resist any change to the voting method. Anything else might undermine their duopoly.
Indeed, and I like this set of visualizations to demonstrate that: http://zesty.ca/voting/sim
This alone is ample reason for those two parties to resist any change to the voting method. Anything else might undermine their duopoly.
So we know why the major parties would oppose voting system change. Is there something beyond the parties' word that keeps non-partisan members of the public from wanting to change voting systems?
Members of the public who want voting system change end up with members of the parties proposing superficial changes to relieve that demand that pose no or minimal challenge to the partisan duopoly, like nonpartisan redistricting (adopted in several states), California's top-two primary system, term limits (adopted in lots of states), tweaks to election scheduling, ballot access rules, etc.