A lot of the trouble with the discussion about attunements is that there are actually four or so separate types of attunements, and each has different pros and cons. But everyone conflates all the types, and mixes them up, so it seems like they are talking past each other. A pro from one type gets countered by a con from a completely separate type.
Here are the types of attunements, as I see them:
Class A: Only one person needs a key for the instance.
Examples are Keys for UBRS, Eye of Eternity, Nightbane in Karazhan
The main advantage of this class is that you can take people who aren't attuned in the group, while still gating access on the whole.
The disadvantages are that if the attunement is too long or difficult, then no one does the attunement, instead relying on someone else to do it. Vanilla WoW players will remember "LF1 UBRS, must have key". If the attunement is too easy and a large portion of the population has it, then it might as well not be there, until you hit the unexpected situation where no keyed person happens to be in the raid. It also makes the raid very dependent on the presence of the keyholder. No keyholder, no raid.
Finally, a group may "purchase" an unlock from someone else, effectively bypassing the gating. Not to mention that I don't think this method can work with an automatic group finder. How could you sign up for a raid if your access depends on someone else in your group?
Class B: Non-raid quest line is required to unlock the instance.
Examples are Molten Core, Blackwing Lair, Karazhan attunements.
The advantages are that you can work on your attunement on your own time. It also ensures that the player does a minimum amount of previous content before they can raid. It's a really good answer the question, "Am I ready for this raid?" A new max level player can also be powered through the questline.
The main disadvantage is that an absolute fresh 80 cannot be brought into the raid at all. Each character must be attuned. As well, if the attunement chain is long, then redoing it on alts becomes rather frustrating.
Class C: Defeating previous raid bosses is required to unlock future raid bosses.
Examples are needing Kael and Vashj to unlock T6 in TBC.
The advantage is that you can't skip hard bosses to progress. Raid progression is "hardcoded" for individual raiders.
The disadvantages are that it causes a lot of problems with raid composition, even before we look at recruiting. The thing is that you want to attune your entire raiding force, including your people on the bench, not just the 25 people in the instance at the time of your first kill. Otherwise, you can't actually progress to the next instance, because odds are you'll have to replace at least one person on your next night of raiding.
As well, it causes large problems with recruiting. Basically, it's very hard to work on attunement on your own, you have to rely on the group to attune you. So already attuned players become very valuable, and guilds have to keep running old content in their limited raid time to attune new players or alts.
Class D: Running old content multiple times eventually unlocks new content.
An example is gating by reputation, like the TBC heroics, where you needed Revered reputation to buy the keys.
The advantage is that you can almost certainly guarantee that people will be properly geared and prepared for the next level of content.
The disadvantage is that it can seem repetitive and grindy (Lower City rep, anyone?). An artifical roadblock to make you waste time. Also this scheme usually has the longest time between hitting max level and actually being able to enter the instance, and people might get bored and drop out early. Personally, I don't think I ever got all my TBC keys.
I actually like Class B attunements. I enjoyed the MC, BWL, and Karazhan questlines, and rather miss them. They provided direction for a new max-level character, instead of having to figure out if your gear was "good enough". Sure, they had some issues (Rexxar, where are you?), and occasionally not being able to take someone to a raid because they where not attuned hurt. Of course, if that happened, the player was always attuned by next week, often with the help of some of other raiders.
By and large, I thought Class B attunements worked. They made the game between leveling and raiding more interesting, gave it more purpose rather than simply gearing up. I would not mind seeing them brought back in a future expansion.
But for Class A,C, and D attunements, I think their problems outweigh their advantages. I think the game is better for having gotten rid of them.