That "anthropic principle" goes out the window pretty quick in book 2 when a super-powered mutant becomes the antagonist.
Premise: You can't expect predictions to stay true over centuries, you need a guiding hand to keep that top spinning and not tumbling over, so you need the Second Foundation to be The Management. Bonus: due to the circumstantial requirements, you get to make them secret and hidden.
Requirement: There has to be tension within a book. There has to be conflict, resolved in a way conducive to literary imperative.
Resolution: Something has to be able to challenge this otherwise-perfectly-set-up system. Something that is not predictable, and which would not be easily adjustable by the Second Foundation; something out of the ordinary. A single man, who really can influence history. The Second Foundation would be prepared for a Napoleon of their time, but they wouldn't expect anyone like the Mule.
Corollary: The Second Foundation is exposed, introducing tension and conflict for the next book in the series. Who wants to be a puppet on a string, after all ?
It could have gone very differently if the Mule hadn't been sterile, or could have taught his skill, but again, literary imperative dictates that "The Good Guys win", so the Second Foundation overcomes the Mule, and the plan is put back on track. Suspiciously well, in fact. The anthropic principle is validated, and a single man did not in fact change history. This time.
"The Good Guys" changes in later books, of course, and the Second Foundation end up losing, but that's quite literally another story :)
What I found endearing about the books[0] is that it didn't try to cast any of the factions as The Good Guys. The Foundation definitely isn't. The trilogy, especially the first book, shows the Foundation applying plenty of hard realpolitik to survive and expand; they do not carry any moral banner, except that of Seldon's Plan. They're not the United Federation of Planets by any measure. They just are. The Second Foundation isn't presented in a better light either.
> The anthropic principle is validated, and a single man did not in fact change history. This time.
I most likely haven't read far enough into the book sequence, but at least by "Foundation's Edge", the anthropic principle remains valid; the protagonist of that book, despite being seen as special by their contemporaries, still turns out to be involved in the story only because they happened to be best person available along the criteria of the ... entity ... driving the events.
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[0] - That I've read so far, i.e. the trilogy, and "Foundation's Edge".
That's why I had "The Good Guys" in quotes :) We're supposed to root for the Foundation/Second Foundation, but it's clearly presented as the best of two evils. People, being people but better than 30,000 years of anarchy.
That's where your anthropic principle ends, though, halfway through the trilogy. From there on out the original protagonists can't win without a new "special" set of characters blessed with superhuman abilities.
(spoiler) Even the entity, beyond the Second Foundation, who started everything and keeps it on track.
In this logical recursion you have to keep track of the level your are in till ultimately a simple explanation is revealed. Sometimes it feels too much of a coincidence, but I enjoyed the mental gymnastics.
It wouldn't even be that bad if the show wasn't regularly referencing back to Seldon and psychohistory, essentially telling us one thing, but showing something completely opposite.
It's not all bad, though. There are elements that would fit well with the books. The way they handled emperors, for example.
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[0] - https://en.wikipedia.org/wiki/Anthropic_principle
[1] - Or what could be described as pivotal moments - the whole point of Seldon's use of psychohistory was to set the initial conditions to ensure there's a high probability that future events will take a very particular path[2]. Kind of like we do space missions today, where a probe is launched just right, so it stays on a predetermined path through the Solar System, making it reach its destination years or decades later.
[2] - And to my great relief when first reading the trilogy, Asimov wasn't dumb about this. He seemed to have known enough about what today we'd call non-linear systems and chaos theory, that he addressed the obvious problems of psychohistory and long-term stability of Seldon's plan in the trilogy (as well as in subsequent books).