Yes, it’s true the two parties fear RCV because it opens the door for a possible third party to eventually get elected.

However, RCV eliminates the spoiler effect; it doesn’t exacerbate it. What actually happens in states like MN where RCV has been fairly widely adopted is that parties that mostly align on core planks collaborate, and tend to be more polite. For example, under RCV, Harris would be motivated to cozy up to Stein in the hope that Stein’s voters would pick Harris as their second choice - votes she’d then get when Stein is eliminated as a distant third.

In fact, under RCV Stein would probably would get more votes; she might even make it into the double digits, but even so, it is most likely she’d be eliminated in the first round.

You’re absolutely right that it’s not in the Dem or Repub partys’ interest to support RCV, because it does give third parties a chance - one they don’t have right now. Even the Tea Party had to give up trying to do their own thing and instead just took over the Republican party like a cordyceps parasite, and they were far stronger than the Green Party.