The constitution (including amendments) is almost unique in that it makes actual guarantees about your right to freely express yourself, even if you views are controversial and out of line with the views of the government. That doesn't make it divine, but it does make it special at the moment. Hopefully the rest of the world wakes up, but I see few signs of that happening (although Dominic Raab in the UK has indicated that freedom of expression will be the top priority when laying out the British Bill of Rights which has been promised since brexit).
American Civil Religion is a powerful drug. Funnily that and their deification of "The Founding Fathers" smell a lot like the absolutist models of Kings and their Divine rights, while being the opposite.
We recognize the Founders for having the courage to throw off the yoke of an oppressor, and succeed. We honor them for then in the same lifetime laying out a blueprint of government that has reasonably withstood the test of time and managed to remain flexible in spite of some serious adversity.
Is it showing it's age? Probably, Is it long overdue for a strong reaffirmation? Probably also. Does it instill in any one particular dude the absolute unquestionable right to rule over anyone else? No. No it doesn't.
The American Experiment, though the institutions of today hedge more on the side of "we'll be the judge of whether you can do that" was fundamentally a novel effort at it's time. It enumerated the Governments specific powers and limits, then dumped the rest of the power in the people to do with as they will.
I mean the first comment literally said "America is the only country with such views" so yes, that makes them special by definition? Or are you saying that the way America sees free speech is common, which would contradict the earlier claim that it isn't