The unfortunate reality of censorship is that it allows ideas to be rewritten because the past has vanished. Re-branding doesn't even require a name change. Take a look at Wikipedia; even though controversial topics may be locked down or contain some bias there is a history of the edits. Who said what when.

It makes it easier to paint a rosy picture of your cause when the previous stuff you said has vanished from public view. It is very possible that censorship of ISIS content on Twitter (I'll take an extreme example) actually has made it easier for them to spread. You are both able to rewrite history and harness whatever in a human brain likes things which are forbidden (aggressively used by musicians and entertainers for decades in the West to market to a younger audience.)

The biggest weapon against people with really bad ideas is definitely an undeletable history. In Europe, they no longer have that tool.