One of the major reasons why Diablo 3 lacks the "social feature" from Diablo 2 is the way in which the "game rooms" (for a lack of a better phrase) are set up. Players are not allowed to create their own games with their own names. Instead, we're left with a "public game" feature in which we join games with strangers strictly for specific quest purposes. Why not let us have the ability to join games for other purposes? Why can't we have the ability to make a game titled "Act 3 Exp Run" or "Act 1 Key run"? Another example: in the current stage of Dueling in the PTR, we are limited to using the PVP channel to find people to duel with. This is highly inconvenient. I liken it to the old trading channels from Diablo 2, in which one would continuously spam what they want to sell or buy hoping a potential buyer/seller happens to be in the same trade channel as him/her. If Blizzard chose to improve upon the old trade channels by giving us an auction house system, why did they regress on the "create a game" function? Why can't we be allowed to create games titled "melee duels" or "monk duels" or "barb duels"? Why are we forced to spam a PVP channel to to search for the people we want to duel?
Another issue with the current state of Diablo 3 is the limitation regarding the number of players in a game. Long story short, the 4 player limit needs to be increased to at least 6 or 8. Granted that I no longer have a personal reason to advocate for this modification due to the fact that only 2 of the 25 or so people on my friends list still logs on, I believe that this increase would help facilitate a better social environment.
Furthermore, there has to be more incentives to actually play with someone else. Maybe an increase in exp gain for playing in a group or something of that nature would accomplish this. Currently, I feel like players are punished for playing in groups. For example, back when paragon levels were first released and some of my friends still played, there was no incentive for us to party up to do our exp/legendary/elite runs. On the contrary, there were many reasons to avoid group games: some members don't move as quick as others, disorganized members would kill mobs that are out of the "exp range" of the other members and as a result, exp would be lost and/or items would be overlooked. In short, the current risk vs reward system of group play highly favors solo play.
To summarize, the 4 maximum players per game limitation, combined with the aforementioned lack of a "create a game" function and lack of incentives to play in groups, all have contributed to why Diablo 3 has turned into a ghost town. I'm sure there are lots of people who still play this game, but the game itself does not provide players with many means to "make new friends." Thus, as each of my friends quit the game, their respective spots were never replaced by someone else. As a result, it seems like I log onto Diablo 3 to play a single player game, which consists of doing 1 or 2 solo modified Alkaizer runs followed by a brief review of my auction house items.
Feel free to add additional ideas/changes you feel would help "revive" this game.
Edit: There are also reasons why Blizzard should strive to improve the social aspects of this game. Better social environment in game = more clashes of egos = more reasons for some people to use the RMAH = more profits for Blizzard.