And
Nazgûl were exceedingly tough:
Legolas shot one out of the sky along the
Anduin, and though it fell quite a distance, it wasn’t killed. (Nazgûl didn’t like fire, but that might be because it was not only painful, but it may have taken them some time to recover from the effects of burns.)
In reviewing this thread in the course of looking for something else, two of your statements here made me want to add:
1-- I didn't get the impression that the Winged Messenger fell quite so far; in fact it seemed to be flying directly overhead and low -- it was apparently about to land on the opposite bank, after all. A minor point, really, as we'd already seen them washed away by the great flood, without damage.
2 -- As to the fear of fire: I have to wonder if the
Nazgul could be "burned"; it's true that
Strider says "they do not love it, and fear those who wield it", but is this from fear of the fire itself, or because of the light it brings? Their power of fear being greatly increased in darkness is mentioned several times; they sometimes seem to be slightly weakened or disoriented by the light of the sun.
On the other hand, their robes are real robes, as
Gandalf tells
Frodo, and apparently not "magical" in any way, so vulnerable to burning. That might not seem very important, except for Gandalf's admittedly ambiguous, yet tantalizing, references to them, that they wear them to "give shape to their nothingness", that after losing them in the flood, they were forced to return to
Mordor "empty and shapeless", and that their power to cause fear is increased when not wearing them. That last, and other statements regarding them, would indicate that they needed them as a sort of control over the fear they instill; their loss would hamper their effectiveness -- especially on a "stealth mission".
As for Gandalf's fire, referenced in the note, that was clearly of a different kind altogether; "like lightning that leaps from the hilltops" is the way Strider describes it, and "lightning" is echoed by Gandalf himself, in describing how people would have seen his fight with the
Balrog. His "fire", whatever it is, is "magical" -- or "holy", depending on your viewpoint.