>>1987253Their special ability is what they get from their wish, not necessarily their weapon, unless it so happens to be tied into that. Mami's real power is her ribbons, she had to design the rifles herself afterwards, for example. Kyouko's spear doesn't seem connected at all to her original power of enchantment and illusions, and who knows what's going on with Madoka's bow. Homura's mechanical clockwork TARDIS shield thing is about the only real example where it's one and the same.
Sayaka's wish-derived ability is superior healing and regeneration, she just happened to end up with the sword somehow. Maybe it just happened, maybe it was a choice, who knows.