> You are told explicitly at the beginning what the type of the result will be
I would argue that's a downside: you have to pick the appropriate data structure beforehand here, whereas .distinct() picks the data structure for you. If, in the future, someone comes up with a better way of producing a distinct set of things, the functional code gets that for free, but this code is locked into a particular way of doing things. Also, .distinct() tells you explicitly what you want, whereas the intention of set() is not as immediately obvious.
> There are no intermediate results to think about
I could argue that there aren't really intermediate results in my example either, depending on how you think about it. Are there intermediate results in the SQL query "SELECT DISTINCT Author FROM Books WHERE Books.PageCount > 1000"? Because that's very similar to how I mentally model the functional chain.
There are also intermediate results, or at least intermediate state, in your code: at any point in the loop, your set is in an intermediate state. It's not a big deal there either though: I'd argue you don't really think about that state either.
> and no function call overhead
That's entirely a language-specific thing, and volatile: new versions of a language may change how any of this stuff is implemented under the hood. It could be that "for ... in" happens to be a relatively expensive construct in some languages. You're probably right that the imperative code is slightly faster in most languages today, and if it has been shown via performance analysis that this particular code is a bottleneck, it makes sense to sacrifice readability in favor of performance. But it is a sacrifice in readability, and the current debate is over which is more readable in the first place.
> a single pass over books
Another detail that may or may not be true, and probably doesn't matter. The overhead of different forms of loops is just not what's determining the performance of almost any modern application. Also, my example could be a single pass if those methods were implemented in a lazy, "query builder" form instead of an immediately-evaluated form.
In fact, whether this query should be immediately evaluated is not necessarily this function's decision. It's nice to be able to write code that doesn't care about that. My example works the same for a wide variety of things that "books" could be, and the strategy to get the answer can be different depending on what it is. It's possible the result of this code is exactly the SQL I mentioned earlier, rather than an in-memory set. There are lots of benefits to saying what you want, instead of specifying exactly how you want it.