What I envision is essentially a team-based game mode that ranks teams based on all kinds of interesting statistics. You jump into Bnet, and create a game with your team members. You then proceed to run the selected D3 quest as a team. The team is then measured on clear times, damage dealt, damage taken, loot/gold earned etc. Your team is then ranked accordingly. You can then compare your team's performance in quest X against the performance of others.
As I see it, the one serious obstacle to this sort of thing is the random dungeon/encounter element that makes Diablo so replayable. My solution to this is straightforward: create a single "build" for every quest that persists through every team ladder season. Competitive teams will then be able to practice the same dungeons over and over until they achieve surgical efficiency. On the other hand, the randominity could very well be ignored, and teams would have to deal with the random construction of dungeons and encounters as an integral part of the competitive co-op experience.
A team-based ranked co-op game mode would be a great way to please competitive Diablo players.
I am eager to get some good feedback, and encourage the community to discuss.