Guilds. All the social interaction you are looking for, you can find in guilds. Guild runs, guild chat, etc. Blizz wants you to join a guild for many reasons, the main one is, if you socialize in a guild you are far less likely to quit.
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Problem is, between LFD, LFR ect, there isn't much incentive to join a guild unless you're tackling difficult content. However, the difficult content is so heavily scripted now and so "broken down" in terms of sharing difficulty amongst the raid, that everyone in the raid has to be a decent player. This forces guilds who actually, you know, RELY on guild socialization, to pick people based on ability, rather than social skills. That's why you have three guilds in WoW right now. Giant level 25 guilds full of people who do their own thing, or high end uber guilds and uber feeder guilds. There used to be all kinds of different niche guilds, because you could play with bad people as long as you had a strong core--and because so many things in the game required your guild interaction.
All that being said, I'm not a huge fan of absolute forced interaction. You're not going to see me saying ZOMG IF YOU SOLO YOU SHOULD DIE!!!!!!!!!!! No. But I think, right now, there is too much incentive to do things through artificial mechanics. Like difficulty...Having difficulty sliders is absolutely retarded. Go back to MC difficulty. Were the bosses there simplistic? Yep. Did a lot of them only require gear? Yep. Was the most important thing in an "uber" guild not actually skill, but rather efficiency in clearing trash and organization? Yup. And you know what that all lead to? People being forced to rely on guilds BUT guilds being ALLOWED to rely on people that weren't great.
By setting the difficulties in this foreign and obtuse way, you deconstruct the need for a lot of the social benefits in the game--because the computer handles social interactions. The damn difficulty slider took the job of the "core" in most guilds (Except high end ones.) This is the problem with using "outside", artificial systems, to solve in game problems. The developers should always look at a problem first and say "How can I fix this where it makes sense in the world."
That's the question they never ask themselves anymore, and it shows. It really causes a lot of problems in the social end of the game, because your world feels like a giant set of steam games, like Gecko said--except instead of the steam chat, it's connected by StormWind. Blizzard used to be like that great DM that just fucking loved making worlds--the one whose favorite part of the game was thinking up cool weapons and bosses, and characters. Who didn't give a fuck if you screwed with his story or how he "thought" you should play--because he never had any idea how you would play. His only job was to create the world, throw stuff at you and watch the fireworks. THAT is the magic these developers have lost.
And like I've said before. I know LFG and all is needed in modern MMO's. I'm not advocating a return to full on EQ. I'm saying there are middle grounds that were missed. Everything in MMO's feels like it's done to excess. And I mean everything, from having so many abilities that even with Alt/Ctrl I can't fit them all on my keys, to a bland, dull loot system that makes the Hammer of the Fire God hit as hard as Orc PvP Blade B, all in the name of excessive "fairness".