What I would have done, coming off of Diablo 2, was to expand upon the interaction between people when it came to the enchantress or baal runs without bots.
The enchantress
This was a social element where a sorc could plan out a special enchant build in order to buff the damage output of low level chars. Where you really want to do go with this is to set up a special type of game where high levels can do something to open up special gameplay for low level chars. The high level player might get a reward in return. This would encourage social interaction as high level players and low levels players are encouraged to interact.
There might be a special dungeon with special treasure at the end. it is only for low level chars but only a high level can clear the zone to get it. Maybe have a special game mode where a team of high level chars can clear a sequence of quests and in the end it opens up a special act that helps low levels. This game would be public and anyone could join and it stays up for an hour. You could login asa low level char and see if any of those games are in progress or have been completed.
Baal run style games (without bots) in Diablo 3.
The social appeal of these games is that you could work as a team to find the path to the area with the treasure. You'd warp to WSK2 and everyone would try to take a different path as they looked for the stairs. A lot of the guesswork was removed by bots, but without bots you can dream up some interesting playstyles. Maybe there are several tokens strewn across a map. Everyone goes their separate way to gather a token. Once everyone has a token, you compare tokens. Depending on the tokens you have found, you have a path thru some special map. Each token has an ability and each player must use the token correctly at the right time to complete the map and reach the treasure. So you might talk with each other about how to use your token in the best way, maybe even swap tokens with someone who knows how to use one very well.
All of this likely requires more than 4 player games to get interesting. But this the general direction I would have taken the game to make it feel much more rewarding. As it stands, you just group up and run a rift mindlessly pretty much and no one says a word.