When you start to add conditions/exceptions to free speech, it ceases to be free speech. Unpopular speech, however painful/nauseating, is explicitly protected in the U.S. If all speech was agreeable, there'd be no need for free speech laws.
Yes, targeting individuals by telling them you are going to kill them is not protected by the first amendment lol It has nothing to do with
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
So, yes, from this perspective, freedom of speech exists to protect Holocaust deniers.
The idea that the Holocaust deniers will "create a new oppressive government" seems extremely paranoid to me. I don't think there are very many Holocaust deniers and I also expect that, somewhat unintuitively, banning Holocaust denial would create more neo-nazis. Banning an idea confers a certain amount of glamour.
I find it unlikely that a tiny minority that most Americans find utterly repulsive could "create a new oppressive government". It's like being worried that a UFO cult will take over the country.