Um.... If you're so sick that you can't even move, then, well, waterbenders DO need their arms to bend. Airbenders, however, can use their breath and, therefore,maystill have a chance to get back in time. Or else, there's no hope.
*SPOILERS FOR BLUE SPIRIT, SEASON 2, AND SEASON 3 BELOW*
And if it's someone else, an airbender can easily grab some medicine and return to the person, like in Blue Spirit! And waterbending can't heal EVERY wound (unless it's special water, like Katara's patch from the North Pole which was used to resurrect Aang).
Plus, a common forgotten aspect is that not all waterbenders can heal! Katara's gift only occurs every so often. I don't even think Aang can heal! Nor is it instantaneous, depending upon the wound. Aang is still hurt from Azula's lightning even after Katara healed him.
Of course, waterbending is still amazing due to this possibility, its supreme defense, and its superior offense. I say that it is the most powerful element (Katara wiped out the entire Dai Lee in one move during the Season 2 Finale,the Swamp Dwellers can bend the plants into huge Swamp Monsters, etc.) if you're skilled enough.
*END OF SPOILERS*
'Course, airbending stillblows me away (literally)!