If fluid intelligence doesn't help me learn stuff faster, is it really worth having? Doesn't it seem likely that learning things makes you better at learning things? If this is true, could an increase in fluid intelligence be the mechanism for it?

Well... I suspect we may be having vocabulary issues here. Gf is defined as "the capacity to think logically and solve problems in novel situations, independent of acquired knowledge."

If your existing Gc already applies to a situation - say, your algebra applies to the economics you're learning - then to some extent the problems of economics are not 'novel'.

It's only a pure-Gf problem when the problems are highly novel. In that case I find it intuitively plausible that a lot of irrelevant Gc wouldn't help much.

Example: if I memorize a couple thousand English words (pronunciation & definition) for the GRE for a large increase in my Gc, why should I expect any increased ability to write proofs in mathematical set theory which will initially draw on Gf as a strange and alien subject?