This is not an example of the thing I’m talking about. I’m talking about 3rd party Senate and House candidates, where you routinely have votes in places that are R+20 to R+50 or the flip for Dems. To have a centrist candidate tip a race like that to the underdog is basically impossible (note - a third party candidate attacking from the flank could tip the balance by stealing votes exclusively from the favorite, but I’m talking about someone in the middle drawing votes from both sides).
Your argument presupposes that nearly everyone who votes is either a diehard for an established party or a temporary voter for whatever candidate. In my scenario of a true centrist party, there would also be diehard centrists.
Even if a few favorites lost to the “other party”, that doesn’t mean a 3rd party that actually stood for something would be unstable. If the party meant anything then it would think the candidates from both parties were unacceptable, so it wouldn’t really matter if the winner was a bit less popular than the other loser. In other words, the “third party” would be a different party depending on the makeup of the electorate, so not all mismatches would be the fault of one party that people then rationally abandon to get better outcomes.