
Most of us would agree the LFR and LFG has made this game less social. Which would make sense that given all the access abilities were given its easy to not need any players and back in the days without LFG and LFR it was so painful to find group members only to have them leave. Now we have the ease of having a tool find them for us and replace them for us and it is a great tool and we should appreciate it. This is a quick set of ideas a few tweaks and additions here and there that I thought off with what could make the LFG experience more sociable.
These ideas are still fairly trivial to killing a boss but it would just make players beneficial for each other if they just communicate. Instead of relying on silly nerf debuffs and buffs they should learn to make better use of their allies to make up for weakness. There should be no need to use these to be able to beat a boss, if your good enough you can beat them like you did before, but team work can come in really handy weather your good or bad.
Also it should help full fill the fantasy of a group of people preparing for a deadly assault (A Raid).

Remove the teleport to Dungeon Feature: You have already eliminated the main problem of finding a group, these is another feature that takes away gameplay in replacement of accessibility. There arn't much use for the vast open with the introduction of this feature. It takes away plenty of the adventure and emphasis of a dungeon! Takes away the sense of danger, the sense of journey and the sense of significance of a raid or dungeon and taking the bravery to journey to it should be a +1 to a players dedication to a group. Blizzard should give some time for the members to corporate and get a sense of each other before even entering into a dungeon. Let them summon each other and just let the players appreciate the adventure for crying out loud we all have flying mounts this should not be a worry.
One of my fondest memory of dungeons is running through the dungeon entrances of Wailing Caverns and I remember how epic it was to finally run through that portal.

-Remove The Luck of the Draw: LFG has become a normal way of picking a group. It is a great way, and it is a fast reliable way of finding what it is your looking for, but this buff just makes players always 5% stronger than the dungeon. That 5% should be made up with better cooperation.
-Group Buffs: A trio in a group band up to cast a power spell amalgamating into a powerful and unique buff. Each class spec combination would results with distinct spells. The sight of seeing a trio of powerful heroes could look like a ball of clouds , sparking with holy light, electricity and arcane, or a demon in shackles and a pair of holy swords and a rogue to gut the sacrifice, or it can merely be 3 warriors doing pep talk yelling at the raid with tenacious fury.
This buff will buff the entire raid. Each buffs are as powerful as each other but different buffs are useful for different situation.

-Warm up duels: A quick duel to warm up your character. Increases all stat by 1% for the loser 2% for the winner. Warm up duels only go down to 50% of the health and cannot done unless in full health. This is done to make it quick and for safety measures of having some guy pulling a monster and 1 shutting duelers. This feature is only available in dungeons and raids.
Maximum buff only up to 5%, last for 30 minutes. Not do-able in combat, automatically cancels at combat. Last after death.
- Synergy of Progressions- A colaboration between two different tradesmen in an effort to make something special. Mixing an engineer and a cook to make a food extra crispy or a Blacksmith and an enchanter to give a warrior's sword a buff.
Examples:
Engineer + First Aid: Band Aid Dispenser (Clickable for a band aid effect, Requires: 5 band aid, 3 Mineral bar, 2 bolts and a hammer)
Enchanting + Tailor: Magic Blind Fold (Increases spell power and spell hit rating, requires 5 magical dust, 5 pieces of cloth. Equip to Head Piece)
Fishing + Enchanting: Mutated Bait (100% chance of a bite and turns it into a mutated fish give 5% run speed, 5% Spirit)
Taloir + Enchanter: Cozy Leather blanket (Gives a 10% Health and Mana/Rage/Chi/Energy/Focus Regeneration and 15% Stamina increase. Requires: 10 Bolts of thread and 10 Leather. Make sure to give this a weak member of the group. Apply to Cloak.
Flavor Text: Oooo, So Warm <3)

-Profession repairs - Give profesions a cooldown ability that allows them to repair specific armor types every 1 hour with a tiny cost of a mineral bar, or material based on the item level of the item. Can repair 3 items per cooldown.This ability is only activated on a group.
Blacksmith Repair Plate
Engineering Repair Mail
Leatherworker Repair Leather
Tailor Repair Cloth
This is done to minimize the need to go outside the dungeon and repair or spend money on a repair bot. 30g is still a valuable amount of gold and I think someone would appreciate it if you save them 30-90 gold.
-Reduce the wipe Debuff:This debuff just goes against the idea of adventure before loot and with this powerful debuff it can reduce the players interest to learn boss fights significantly. I think this is a good for LFR players but I think the slight push needs to be more slight, making the debuff for wipe only 2%. If you wipe 5 times 10% is already massive debuff.
- Philosophy of Need is Rule : game design that is make sure compliment practically over players personal conveniences and personal greed.

This thread is also dedicated in memoriam of dungeon entrances. You will be missed.