...and was then asked at every turn, by every website and application and whatnot, to provide four or more digits of this number to accomplish even the most benign things.
There's what the US government thought it would be and then there's what it's become because zero enforcement on use of it as a national person identity number was ever enacted.
The "don't give anyone your SSN" trope has become one of those household jokes. Right up there with "American's don't pay high taxes".