Does invoking Hitler work as a rhetorical strategy?

I am not certain that this tells us all that much but it is pertinent to a topic I have mulled.

The topic being the casual accusation of "Hitler" against arguments strong and weak, opinions absurd and well-founded, and facts of any of a variety of stripes. If you don't like a person or their argument it has almost become de rigueur to invoke Hitler.

A phenomenon so common it has spurred adages and laws. For example Goodwin's Law.

Godwin's law (or Godwin's rule of Hitler analogies) is an Internet adage asserting that "As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches 1"; that is, if an online discussion (regardless of topic or scope) goes on long enough, sooner or later someone will compare someone or something to Adolf Hitler or his deeds, the point at which effectively the discussion or thread often ends. Promulgated by the American attorney and author Mike Godwin in 1990, Godwin's law originally referred specifically to Usenet newsgroup discussions. It is now applied to any threaded online discussion, such as Internet forums, chat rooms, and comment threads, as well as to speeches, articles, and other rhetoric where reductio ad Hitlerum occurs.

There are many corollaries to Godwin's law, some considered more canonical (by being adopted by Godwin himself) than others. For example, there is a tradition in many newsgroups and other Internet discussion forums that, when a Hitler comparison is made, the thread is finished and whoever made the comparison loses whatever debate is in progress.

My disdain for arguments culminating in reductio ad Hitlerum is that, in addition to being mentally lazy and ignorant, they trivialize a still almost incomprehensible tragedy. Just because you disagree with someone or because they won't give you what you want, does not make that person Hitler. Making the reductio ad Hitlerum argument is a testament against you, not the person with whom you are in opposition.

But Justin Murphy is investigating a different question. Does the reductio ad Hitlerum argument work? Is it an effective argument? His findings are suggestive but not conclusive: this is just an early step in research. From What is the effect of comparing Donald Trump to Hitler? by Justin Murphy.

Our study suggests that comparisons to Adolf Hitler’s policies may not undermine support for particular public policies today. Future research should consider whether the effect of Hitler comparisons might be conditional on the political ideology or partisanship of the individual. Previous research suggests that conservatives or Republicans may respond to such analogies with increased support for President Trump and/or his administration's policies, whereas leftists or Democrats may respond with decreased support. A limitation of this study is that we did not measure ideology or partisanship so we could not explore this question. A future study should explore this possibility.