Being able to switch difficulty modes mid-game is what has allowed me to experience some excellent stories that I otherwise would not have been able to.
AnorakTheClever, via Twitter

The decision on which difficulty level is most appropriate is often as a result of trying to play the game on the default setting.

Allowing a choice during gameplay or upon death means being able choose to play at an appropriate level without having to lose your progress so far.

This can also be achieved through adaptive difficulty – dynamically adjusting the difficulty level according to the performance of the player.

Best practice example: XCOM: Enemy Unknown
Best practice example: Braveland