A pure mortal, the average person doesn't have supernatural power to back them up, in response to this deficit a person has to rely on what made us the dominant species, ingenuity, guile and creativity. For me I see part of that extra refresh bonus as being an extension of that mindset, its extra stunts or a few extra aspects invoked in a game session, it reflects the outside the box thinking and resourcefulness that makes people people and how they manage to win or survive against the bigger faster meaner things that go bump in the night. But give a man a hammer (or sword) and every problem starts to look like a nail.
A mortal with a supernatural power is going to start seeing the world in terms of 'how can I superpower my way to victory?' Once you have that power you start to try and 'game' everything towards your strength. Options that don't rely on that advantage stop being considerations and your world view starts to shrink. The bigger and better the hammer, the more you try and make your problems a nail, and those hammer free solutions fade completely from view. This is how a person becomes a monster, how they loose their free will and how they use up their refresh.
If you're giving a character a real supernatural advantage like a powerful magic sword, then you should make them pay for it just like any other hammer in the tool box, regardless of the narrative justifications for it. He's still going to be seeing his problems as fencing dummies. "I got it from my brother" and "I got it from my faerie father" just the mode of transition rather then the fact that its magic and its family.