No. It shouldn’t. And this is horrible town strategy. Town lynching third parties might help them win, but it will certainly help scum win. Barring Serial Killers, which are typically much more of a liability for town, third parties should be left for scum. In fact, I will happily lose to a third party if it prevents a scum win. Because scum will always further their win condition by killing third parties. And town will always further scum’s win condition by lynching third parties. Scum taking out town power roles is icing on a cake. The cake is the kill itself.
So if scum want to play third-party chicken, I will happily play that game with them. Because they don’t hurt themselves by killing third parties. Town does. This is basic game theory. It’s why I (correctly so far) predicted that Crys’s bandwagon was full of scum. (Note: I’m not spoiled yet, so there’s no perfect information.) I have a feeling a few more scum are still on that wagon. Right now as of the reveals, the percentage of scum is noticeably higher than dumb luck.
I don’t think I’ll ever understand Town’s burning desire to take out non-killing third parties.