It has some downsides, though: it's a little stiffer and thus harder to tie knots in. It's less resistant to abrasion (being dragged over rocks, etc.). But it mostly disappears in water.

That's my understanding as well. That said, I hate fluoro line, especially on spinning reels, as the extra stiffness gives it a tendency to want to come off the spool already. Add in any extra "weird" factor like a badly timed gust of wind when casting, and you wind up with a big tangled birds-nest of line wrapped all around your reel. :-(

OTOH, there's a another "superline" formulation out there, that is made of the same material as braided line, but it's fused instead of braided together. The Berkley Fireline Crystal version claims to be nearly invisible in water (similar to fluoro) while still having the strength, suppleness, etc. of braid. I've been using it for a while and have been pretty happy with it.

That Fireline looks interesting.