I can't speak for others, but for me freedom of speech is the
absolute highest right, and the other rights are (for the most part) either subservient to it, or directly supporting it.
The First Amendment grants freedom of speech.
The Second Amendment is useful because it lets you defend yourself against powers that try to forcibly take away that right to speech.
The Third Amendment and Fourth Amendment are useful because they keep the military from moving in (to your property) to intimidate or hinder your speech, or to drum up other charges or steal your property to punish you for your speech.
The Fifth Amendment is useful to keep you out of a Kafka-esque nightmare where you're not officially breaking speech laws, but the government punishes you via an unfair judicial system.
Etc. for the remaining Bill of Rights.
The reason that I personally value this freedom so highly isn't that others should be able to speak, it's that I should have the right to hear whatever I want that others have to say.
If I want to go listen to speeches by a neo-nazi fringe group to understand what drives them, I cherish that right and would begrudge any system that says I'm not allowed to. How can one expect to understand the world of they're not even allowed to hear the words or observe the true personal expression of those they disagree with most strongly?
Likewise, in America the skepticism of government is pretty deep-seated, so I have no faith that granting a government body regulatory rights over some speech which I don't like wouldn't soon snowball into government using those same rights against speech I do like. Better to never grant such decision-making to the government in the first place.
This is just my personal take, so take with many grains of salt, but thought it might be helpful in explaining some of the underpinning American ethos (since I know that stuff can be hard to translate cross-culture)