It's funded by tax dollars, and regulated by local and state laws.

If they want their own private primaries, then it should happen internally and at the parties' own expense.

I envision that it does not matter, because this is a tactic that would 1) be available to all, and 2) it gives up your vote for someone of your own party, thereby weakening your own position. It's self regulating.

Can't they do that now? If I think my chosen primary guy is winning in a landslide I could just register for another party I don't like and vote for someone who I think is easier to beat.

Yeah it's the latter. The US does not have party membership the way that, say, the UK does. In many states, it's open primary. In Colorado, for instance, I get mailed Democratic and Republican primary ballots and can vote by mailing in either one. I think you get neither counted if you mail in both, but I have no idea; I've never tried it.

The last time anyone tried to poison a presidential election by promoting a weaker candidate on the other side in the US, it was the Democrats boosting Trump in 2016. It did not work out.