Are we remembering the same Factbook? It had summary statistics for every country and some brief blurbs about their history, climate, economy, etc. Strictly speaking yeah it generated some legitimacy to publish a resource like this and I find it hard to believe the CIA can't scrape a few quarters together to keep it running, but most of it's value is sentimental.
As an anecdote example, I've never ever accessed said Factbook, but I've heard about it enough times to remember that such thing exists and that USA govt. is collecting a relatively objective fact list. So yeah, it was a tiny bit of soft power of sorts. It showed that USA cares about outside world, in some way at least.
PS: and I live in Eastern Europe, far far away from the USA.
You might be underestimating the reach, you've got schoolchildren around the world using it as it's usually the most convenient source you're allowed to cite for this data
I grew up outside the US. I have a distinct memory of using the Factbook for homework assignments and being told it is a reliable source of information. That shapes people's perceptions of the US and the CIA from a young age.
Soft power includes positive perception. Every time someone learns that GPS is completely paid for by the American government and then freely available to the rest of the world, that shapes perception.
The Facebook being quoted by so many school kids worldwide was a cheap softening of how the world perceived the CIA and America. Now how valuable that is isn’t clear, but when something is that cheap it doesn’t take much to be a net gain.