I've seen a few cases where people have committed suicide after suffering online hate, and to be honest, I don't think that this hate made a radical difference – rather, it was something that triggered an individual who already was in a very dark place.

Sacrificing free speech for their sake of like doing a nation-wide ban on peanuts to help people with allergies: it will prevent quit a lot of accidental deaths, too. Except that peanuts are not essential for a functioning democracy.