In a games scenario, being able to include as many people as possible to play your game is what you're aiming for. Designing the game so people will disabilities or handicaps can experience what other players can experience without those handicaps.
There are a wide range of examples for this, DICE games such as Battlefield or Battlefront (2015) accommodate players whom are colourblind.
Pulled from a reddit post in r/StarWarsBattlefront
This is great as the game slightly changes how certain colours look depending on the profile selected above.
YouTube thumbnail from Battlefield 3 Colourblind Mode Comparison
But you can draw this same conclusion with games that support controller. I'm specifically talking about PC games here, games that are primarily played with Mouse & Keyboard, but has controller support for anybody who wants to play with a controller that may or may not have any disabilities or handicaps. So it's great to offer actual inclusiveness for players who may have something different about them, along with possible control remapping for anybody to use instead of the primary control method.
In the end, it's all about widening your audience.