Is that a reference to 8chan? Because if so I am pretty sure that they removed controversial boards of this form a few years back - long before cloudflare banned them.
You heard wrong.
> But if not - that's good
Censoring people for their attractions/fetishes/sexual orientation is never good - it is bigoted.
It shows you're afraid of their ideas, and the persecution can embolden them or give them a sense of legitimacy. It can being the Streisand Effect to their cause, taking a no-name site no one knew or cared about and blowing it up into something everyone is deeply aware of.
The key word being "kinda". You give the perception of power, but there are plenty of things in society we deal with by a form of "banning" (such as incarceration) in which we judge the ban to be good regardless of the power it gives people, or the ideas they represent or practice. Locking up child abusers, for instance, may give the spectre of child abuse power, and highly-publicized instances may fuel the moral panic around "strangers out to get your children", but that doesn't mean they should not be locked up.
In civil society, we are justifiably afraid of many ideas - I don't know anyone who wouldn't be afraid of a Nazi-style dictatorship, or its prospect. Fear can be a legitimate way of preventing bad things from happening. I fear dying in a house fire, thus I take certain precautions when cooking. In the same way, a demonstration of power over a person or idea may outweigh the power supposedly given to that idea by banning it.
The key is a balance; it may well be that you get an instance of the Streisand Effect, but it has to be shown that the consequences of that outweigh the very material consequences of such ideas coming to fruition in real life. For example, many people don't know who Barbara Streisand even is, and if they do, they likely don't know about the pictures of her house. The very canonical example of the Streisand Effect shows a short-lived controversy about the actual matter and ensuing attention for a few months after the incident. Then people forgot, or simply stopped caring. "The Streisand Effect" is more of a Streisand Effect than the actual incident that created it.
Do you believe that if people with ideas that you consider to be Nazi-like are allowed participate in the public debate as freely and meaningfully as everyone else (e.g. by using electronic services regularly available to everyone else), a Nazi-style dictatorship is likely to come about?
To be clear, I don't advocate for censorship of ideas that I simply "don't like". That's not a sufficiently rigorous standard. Ideas which advocate for targeting marginalized groups, or entire groups of people for ideas they have no control over, are fair game, in my opinion. I don't pretend to have no bias in my answer to that question. I am biased, and others have their own biases. I draw the line where I want to draw it, with no concern for pretending to derive it from first principles.
Do you think that's going to end well? How do you expect those people to feel about you? There is a very good reason why societies have protected the right to political speech, and it is to prevent the inevitable conflict that arises when some people in society feel that the rest of society is preventing them from attempting to further their own interests in the same capacity that other groups are able.
In the case of political speech that you consider Nazi-style, your rationale is that you believe it will make an event you consider to be unlikely become even less likely. You believe it will have a sufficiently large influence on the likelihood to make it worth bearing the consequences of telling people in your society that they cannot participate in the public political debate as freely and meaningfully as others. Why do you believe it would make that event less likely? And why do you believe it would reduce it enough to justify the risk?
2. Admittedly anecdotal, but while bans like these do increase _knowledge of_ said websites, I see no evidence they significantly increase their popularity or userbase.
Again, this is in reaction to literal neo-nazis getting deplatformed.
If your first reaction to seeing nazis get in trouble is to ask "well what if I get called a nazi?" then you might need to do some introspection my dude...
Also - deplatforming is incredibly effective at severely limiting people's reach. Anyone know what Milo Yiannopoulos is up to these days?