Wings are delicate and important. Using pixie dust alone is not enough to support the long and arduous tasks that a fairy must endure on a daily basis. While flying without wings as a fairy is most certainly possible, like with most creatures that use pixie dust other than fairies, it runs out faster. This is why fairies with damaged wings prefer to ride on an animal, as it's much more safe and reliable. Flying with a broken wing
really hurts and is unsafe.
This is because wings absorb pixie dust better than anything else. When it is used to take flight, some is lost over time, but most of it is well absorbed for long periods of time. With other creatures, the dust isn't absorbed as well and some of it shows on the surface on them, never to be absorbed, instead falling off. A fairy can go for at least a day from one pixie dust shower whereas anything else without their wings can go for about an hour of flight. Fast-Flying fairies have a much bigger and longer pixie dust shower for themselves because their talent requires many hours of constant flying, of course!