It'd also be pretty sad if we apply a simplistic solution to a complex problem and make everything worse.

I wasn't answering the question of if we should try, I was narrowly responding to a single claim that laws restricting hate speech would be easy to write because it would simply be a matter of applying existing laws slightly differently. That isn't the case. Irregardless of what you think of the merits, nothing analogous to a ban on hate speech is currently on the books in the US