Enharmonic Keys: Pointless or Practical?

Try this quick exercise: play the first couple measures of the Gb major and F# major scales ...déjà vu?

Both scales are played with the same exact piano keys, so why are they written using different notes and accidentals? Actually, these are two of the six musical keys with alter-egos known as the "enharmonic keys":

• What's the Point of Enharmonic Keys?
• Why Some Keys Don't Exist At All

_{Image © Brandy Kraemer}