Well, the sort of creativity needed to pull a background out of thin air is unlike most other forms, not goal oriented. You tend to see a progression of:
No Background
Goal Based(tight) - Background essentially describing character mechanically
Goal Based(loose) - Background describing character, sans personality, but with integration of non-essential things like setting.
Sweet Spot - Background matches character, with integration into external elements and individual quirks.
Story based(loose) - Background story makes sense in context, but with little to do with character capabilities
Story based(tight) - Story has little to do with setting, rules or character, world of their own.
No Background.
Which end they start from does not depend on their background(arts or science), but on personality. Mechanics heavy games like GURPS and D&D tend to spawn from the top first, while story heavy games like Burning Wheel and other more abstract systems favor the bottom path. So where you start from depends on your personality + your first game.