If it is an extremist thought it is better to know who is saying what than cutting off communication completely and hoping the problem goes away. But this has to go along with society coming together and addressing the problem firsthand. Is the extremist thought because of a mental illness? Is it some monetary issue driving such thoughts? Is it social issues that is driving such thoughts? Is it religion? The thoughts by themselves are immaterial unless the individual is a psychopath. Many turn extremist because of an underlying cause which I call the "root cause". Attack the root cause. That'll fix the person. For how long will society keep ignoring this aspect of human beings? Unless you dedicate funding towards tackling such issues you'll get to no where. By shutting off communications you haven't shut off these thoughts that crop up in an extremists mind. Al Qaeda existed before internet was even a thing. We have had genocides when technology did not exist. All throughout human history. It always has been bloody. On the contrary, I can argue that we are at a much better place than we were in the past many thousand years. So to only blame technology for spread of misinformation is disingenuous. Before technology existed misinformation spread rapidly through word of mouth but there was no way to cross check it. Today you have that ability to cross verify. You just need to give time to people to get used to this.

But once you introduce Censorship there is no turning back. Once authority tastes power they'll want to keep using it more and more. Just like Surveillance, Censorship will become a powerful tool in the hands of the powerful. It always starts with a valid justification.