No, free speech is a natural right. The recognition of free speech is not contingent on any outside factors aside from the recognition that humans speak just like they breath.

> There have been quite a few recent shooting sprees where the perpetrators either explicitly referenced online personae, or the investigation revealed they consumed these sources predominantly.

So? Did these shooters also go to the grocery store? It's ridiculous to ban Coca Cola because a shooter predominantly drank diet coke. You're a) inferring a spurious causation simply because you want there to be one, and b) even if there were a causation, that does not entail that the online personnae are in any way responsible for the shooter's actions.

> The idea that people aren’t influenced by what they read seems somewhat indefensible, anyway.

Who's defending that? The issue I'm raising is who's responsible for someone's actions. Speech is not action. The most widely recognized limitation on free speech is treating incitement to violence as violence. That's perfectly reasonable. Is that the case here? Doesn't seem like it, because if it were, they'd be charged with crimes.