I believe the Wither should add a new layer of challenge to the game once it has been defeated by adding a new mechanic to the game called Wither.
I propose that the Wither, after it’s initial explosion and when it uses its attacks, spreads Wither. Withered blocks would spread over grass and other surface blocks. Once the Wither had spread far enough, the area it occupied would be considered its own biome.
The Withered biome could lead to withered versions of classic overworld mobs spawning, these could include wither skeletons (possibly an archer variant) withered zombies, withered spiders and withered creepers which, when exploded, spread the Wither to any suitable blocks.
The biome could also have resources which could drop from mobs, or generate in the biome. Such as withered flesh from zombies, and withered wood from trees.
Once diamond armour is obtained, the other sets become almost entirely useless. A new armour set should be added made from the bones of withered skeletons, which provides a level of resistance to the Wither effect. This gives the player a reason to have multiple sets of armour and adds a new reason to go to the nether.
The beacon provides a reward for defeating The Wither. In this concept, the beacon would have the added benefit of protecting the area around it from the Wither spread.
Thank you for taking the time to read this post. Vote to see this concept in minecraft :)