I know of a couple guilds on my server that are social, have a raid team, but the guild is more built around socialization and doing random things. ie retro-raids, pvp, dungeons and scenarios etc. They use a chat channel to help bridge the gap between guilds and alts, which is something i recommend, its something I've been using since Wrath and maybe late BC (can't really remember). I have about 4 chat channels that are always going during the day and its a great way to keep in touch and find friends to do stuff.
The problem really is there isn't that much outside of CMs, Raids, dungeons, scenarios and Rep Farms that require a group. I found that Isle of Thunder really was the best return to the old days of finding random people to do stuff. People didn't really chat but it was very similiar to BC vanilla era of needing others to complete something. Our isle was always blowing up chat with where rares were and people looking for help killing etc.
The social interaction is what you make of it. We'll see a little nod to it when we get the "harder" heroics in WoD, but even then most people are established in the game at this point. Thats also a MAJOR factor in why the game early had much more socialization, we were all new and needed to meet people, 10 years later we know people and don't really have to leave our social circles. How often in real life do you go seeking new friends? Most people have an established group of friends in RL that they don't stray from. The same is going on in game, most games don't have a life span like wow, so to say its only because of LFR and LFD is ignoring a lot of other causes to the decline in random socialization. In BC and Vanilla and Wrath people were still "new" and looking for people, where as now people are established and have a core so they don't branch out as much. LFD should go back to realm only that would be the most helpful so at least the people you meet you run into again in the LFD. That is about the most helpful change they could make. LFR is LFR and I have no problems either way with it, but I don't blame it for why socialization is down, do you really want to be friends with people who have no more in game aspiration than completing LFR? Those people are just going to get geared and then stop playing.
Side note, I know for sure there is a ring of people who do a lot in the Pet trading and hunting world and that is a great way to make friends now. Finding people with a similar interest that doesn't have a random way of putting people together.