I'm not sure if these points have been mentioned, I only looked at part of the 400 pages on this topic!
1. Be it an insta-LFG tool, the game's current LFG via the Who panel, or "spamming" general chat, you end up in a group with the same level of comraderie with your fellow group members, namely zero. It's what happens after that's important. If I run several heroics with the same people or have a really good time in a flashpoint with someone, that person is going on my friend list for future socializing and grouping. That's community.
Obviously this doesn't work with cross-server grouping. Cross-server is a band-aid for the wound of faction imbalance and low server population. Separate (and important!) issue; suffice to say I am anti-cross-server LFG.
2. I do like the idea of opting in to cross-server warzones where your whole side is from your server. Not sure how much queueing that would alleviate but I don't see any problems here. If you only want to play against your own server, don't opt in.
3. For heroics, you don't really need the standard tank, healer, 2xdps. Any 4 will work. I heard some people concerned about dps-ers having a hard time and getting booted from auto-made groups, but I don't think it's a problem for heroics.
3.a. But you do need the standard group for flashpoints! However, I think the game is surprisingly well balanced right now in terms of healers, tanks, and dps. Plus lots of classes can fill multiple roles. I think dual-speccing the ability tree with, say, a 30 or 60 minute cooldown on swapping, would make this virtually a non-issue and not take away from the game in any fashion. The last thing I'm worried about when finding a group is class makeup- usually I am just so happy to find 4 people!
TLDR? New group members are strangers no matter what. If you have fun with them, friend them. That's your community right there. Idea: cross-server warzons, but your whole side is from your server. And I support dual-speccing the ability tree.