"book burners" seems like a particularly poor analogy, given that the general motivation is to reduce the death toll of Covid-19, not eradicate a cultural heritage (which was, in the case of the Nazis - the quintessential book burners - accompanied by a deliberate mass genocide). A more apt comparison would be people who lobbied to restrict tobacco advertising (see the Surgeon General's Warning, etc.)
I'm sure the motivation of many book burners of the past was also to save the would-be readers from eternal hell. Possible good motivations don't justify censorship.
You could argue that in this particular case censorship probably won't even be effective. Rogan is seen as a something of a censorship martyr by quite a few people now, Streisand effect and all.
Also, there's the fact that most of the removed episodes have nothing to do with Covid-19.
GP said "modern version of book burners". You say it's a poor analogy and "beyond hyperbolic" (below)... and then bring up the Nazis and the Holocaust.
Were all these deleted episodes just about COVID misinformation? All 113 of them? I haven't listened to them but the other comments on this thread seem to indicate that is not the case at all.
I can't speak to Spotify's odd decisions. I don't really care what they did. But the initial "outrage" was targeted specifically at Covid misinformation.
Either way, the book burning analogy is beyond hyperbolic.
The point is simply to ground the conversation in reality, not in this peculiar language of extremes. Will spreading medical disinformation on a popular media platform kill people? Yes, probably. Is skepticism of mainstream medical narrative healthy? Yes, probably. Are those two things in tension with each other? Yes, usually. Should private platforms restrict content that will probably hurt people? Maybe, I don't know. Is this the moral or historical equivalent of book burning? No.