Here's my 2c on how they should have made it. Instead of expanding on tired characters and storylines, they should have begun the d3 long after Cain and other characters from d2 were dead. Suddenly making it 18 years later, keeping Cain, and having an 18 year old mystery girl become the vessel of diablo, WHO IS ALSO CAINS NEICE, seems ridiculous; like a sitcom where everyone is dating each other because they are running out of new ideas. So here goes...
It's a celebratory time filled with greed, indulgence and excess Diablo and Baal have been vanquished and there is not a care in the world; these selfish behaviours are the driving force behind the return of an unknown evil.
Perhaps a cinematic at the start of the game could show alcohol, blood, spit, and sweat hitting the ground then turning black and seeping into the cracks of the earth, eventually forming a large black, amorphous rotating ball at the center of hell (sorta like the antagonist from 5th element). This ball represents the culmination of sins in the world that have been slowly adding up over time. (These sins are seemingly inevitable and the result of human nature). From this spinning, amorphous ball a face appears, Azmodan, the Lord of Sin. He gives his speech that he gave to Leah in the church, (but without Leah), about how all he had to do was wait as his brothers fell one by one; inevitably, people would bring him into the world because of their selfish and sinful nature.
Act 1: Hell
Instead of starting at "New" Tristram, your character begins in Hell. A light from the heavens shines through one of the cracks and plunges through the earth into hell, awakening a fallen warrior from ages past. Your character is driven by penance; he/she wants to get out of hell, into heaven but must make up for past evils, and stop Azmodan from conquering the earth, and heaven to do so. This light of heaven acts as your guide and the narrator of this story. The first Act takes you through your journey out of Hell. You must battle several lieutenants of hell along with several of the aspects.
Act 2: Underworld
A2 takes you to the place just before arriving at earth. You're essentially in a crypts and underground with all the rotting beings that have slowly been corrupted by Azmodan on his journey out of hell. The quest is to save the souls of many of these beings, stop the further corruption and also get out of there and up to earth
Act 3: Arreat
On his journey through Hell and the Underworld, Azmodan let loose a flurry of demons and undead that have ravaged and terrorized Sanctuary. You are greeted by this terror as you emerge from Hell through arreat crater. This act focuses on emerging from the crater, rallying support, and stopping the flow of undead and demon minions from the crater.
Act IV: Sanctuary
While you have stopped the invasion from Arreat, more invasions commence from across Sanctuary. This Act takes you through several areas all across the Diablo Universe as you attempt to eliminate each of Hell's lieutenants leading separate invasions. Once you've seemingly quelled each one, a messenger arrives to tell you that there are several dozen more. The realization comes that you must defeat Azmodan on his journey to conquer heaven if you are truly to stop the onslaught
Act V: Heaven
I sorta liked the idea of this act from D3 even though it was poorly delivered. This would be a short act that had a very fast-paced theme to it. The idea being that you are fighting a losing battle to get to Azmodan as Sanctuary, and the Heavens, are crumbling against his onslaught. Eventually you reach him in battle. While the hero is able to defeat him, it is a lost war. Having nearly conquered Sanctuary and the Heavens, there is an endless supply of sin for him to be born again anew. You pick up your items, and then the forces of hell descend upon you in the ending cinematic as his rotating black sphere reforms and is fed from the chaos.
The expansion continues on this storyline and is about the journey to discover what must be done to defeat Azmodan in order to retake Heaven and Sanctuary.