We already have laws that deal with explicitly inciting people to violence.

So called "hate speech" generally is not an explicit endorsement of violence.

Wrong. Hate speech, at least in the US, has no formal definition. All it takes for something to be considered hate speech is to call it hate speech.

Incitements of violence are already prohibited by law.

To the extent that speech is dangerous, it's pretty easy to pivot to defending it on 2nd Amendment grounds, in addition to the 1st. (Relevant: https://xkcd.com/504/)