> Being allowed to impersonate others simply doesn't seem to be an important part of that.

You forgot the "allowed to impersonate others to do parodies" part of it. I don't understand how you can be staunchly in favour of freedom of speech while holding the position that this kind of speech, blatant parody humour using impersonation as a delivery tool, is not protected under freedom of speech.

If I somehow managed to register the domain "gooogle.com" and use it for humour, to take jabs at Google by displaying loads of fake ads instead of search results, showing on purpose unrelated results to the search query, etc., should my website be banned?

Impersonation for scams and straight up deception are already punishable under other laws, why is that impersonation for parody and humour should be punished? I thought that was... Speech.