My answer is to the first is: did it work? Did the media successfully block Germany from being taken over by Nazi ideology?

My answer to the second is: why are you even asking this when it is exactly the polar opposite of what I'm suggesting? Of course that's not a fair example at all!

If you go back and reread what I wrote, you'll notice that nowhere did I mention that a "both sides" approach was the solution. Rather, I mentioned that something is badly wrong when a lot of people on one side have the experience of being banned or censored.

Let me give an analogy. Suppose you observe, correctly, that in the United States, the rate of incarceration for black men is 5x the rate for white men. Furthermore, you observe, correctly, that the rate of recidivism is about 15% higher in black men than white men in the first year, and overall recidivism is incredibly high in the first year (half-ish, depending on how you count it; much higher for lifetime rate). You conclude that: we need to be tougher on crime--longer sentences. And you conclude that black culture is just crap, there's no bias in the system (well--you can measure it and there is, but the levels of bias are tens of percent, not 5x; the bias doesn't remotely explain it). Tough on crime! Ghetto culture is bad! That's our answer!

Or, you could say, "What the *(@%&?! 5x disparity? How on earth can this be possible?" And you can go in and look at systemic poverty, and cumulative bias (adds up to more than 10s of percent when you accumulate the disparity in every step), and why are sentences for crack cocaine specifically so harsh, and why is marijuana illegal at all? Wait, people are going in for minor offenses and coming out, in some cases, as hardened criminals?! And you could conclude that the whole criminal justice system is botched and in desperate need of reform; and actually we have some pretty troubling societal problems too that really need addressing. Maybe we don't need to be tougher on crime in the jack-up-sentences way, but to figure out why we have so much crime; and not to negate either the culpability of or the harm caused by people who commit serious crimes, but maybe we need to rethink how we approach dealing with criminal behavior given the evidence from recidivism rates that the current approach in the U.S. is basically a disaster.

You seem to be operating under the implicit premise that people cannot be trusted with ideas: some ideas are dangerous and cannot be remediated, and the only way to deal with them is to hide them. Even leaving aside whether this is practical (given modern technology one would tend to think no), this premise destroys the foundation of democracy. Now, if you want to argue for meritocratic authoritarianism as an alternative, as in, say, China, that could be an interesting discussion. I would argue against it, but it's interesting, and I cannot fully justify my perspective with data. But I haven't gotten the sense that this is the direction you're leaning. I do, however, think that it is a necessary corollary of the premises you need to adopt for more censorship to be a good idea.

In contrast, I think that the problem with Twitter and other social media specifically--there are plenty of problems with the Republican party outside of that--is not that one side is acting up, but that the game is wrong. The system works in a such a way as to make this sort of thing almost inevitable (e.g. lies spread faster than truth: https://news.mit.edu/2018/study-twitter-false-news-travels-faster-true-stories-0308). If the underlying mechanics promote tribalism and falsity, and censorship is expected to increase attachment to falsity due to it functioning as a theat to tribal sanctity, my solution isn't (mostly) to blame the players en masse (though I will scold them one-on-one). It's to change the mechanics.

It's the same logic as one uses for dealing with communities with high rates of crime. I see no reason why it's any less valid just because it's virtual.