A few decades ago, the Democratic party in Southern states was whites-only, claiming that as a private organization it was free to discriminate. Because the Republicans weren't competitive in those days, and the Democratic primary effectively decided the general election, that helped to ensure that if any blacks managed to register and vote, their votes wouldn't mean much.
I don't see how letting party bosses who weren't elected or even appointed by elected officials tell the voters which candidates they may choose from would benefit democracy. The hypothetical abuses of open primaries pale in comparison to the actual abuses that occurred in closed primaries; crossover voting might swing a close race, as happened to McKinney in 2002 (I don't think it was that close this time out), but I don't know of any instances of wholesale hijacking of one party's primary by the other.
In your hypothetical, if the Democrats were so dominant that they could swing the Republican primary their way, then wouldn't they be dominant enough that it wouldn't matter who the Republican nominee is?
" I don't see how letting party bosses who weren't elected or even appointed by elected officials tell the voters which candidates they may choose from would benefit democracy."
It is changing that system that will end democracy.
Party bosses are called party bosses because they run a political party whether it is Libertarians, or Greens or the Constitution party or the Republicans, or the Black Lesbian party.
Let the people form parties then choose a candidate within that party to represent it in the general election, then the public at large makes their chose from those candidates.
To now give the government power over how the people choose their party's candidates can do more harm than good.