It works, kind of, but I would guess that it actually goes in the other direction and that the personality is a reflection of the power, even before it manifests. Claire doesn't quite make sense otherwise, and I don't buy Nathan, either. His power was manifesting itself when Peter was trying to fly way back at the beginning of the season - Peter was siphoning some of it. If it were need/desire based, I would think Nathan would have expressed healing powers ala Linderman to heal his wife.
Or more likely than any of that is that it is easier for the writers to make the characters archetypes and have their personalities make sense with their powers rather than it being something they actively thought out.