Remember how you were taught to eat certain foods from every food group? You probably learned young that while you may be able to survive off of nothing but peanut butter and jelly sandwiches for the rest of your life, it was far from ideal. Health wise, you'd definitely be gimping yourself.
The same principle applies to raids. You could do an entire raid with nothing but Druids, I'm sure. You'd survive, with a bajillion combat rezes. Hell, you'd even be covering the basic 4 food groups of a raid: Healer, Tank, Ranged DPS and Melee DPS. You could go with all pallies as well, though you'd be lacking on the ranged dps.
The point is, you don't necessarily have to have optimum raid synergy or diversification to succeed. Blizzard has really pushed the "bring the player, not the class" mindset since the release of Wrath, though there have been multiple exceptions. None of us healing priests have forgotten the nightmares of trying to Mind Control for the first time on Razuvious. *shudder*
However, the main way that Blizz has worked in this philosophy of raid makeup is by merging various kinds of buffs. They started this in BC, and I really think a big reason for that was the true takeoff of 10 man raiding that was coming in Wrath. Instead of utilizing Shadow Priests as mana batteries, they introduced the Replenishment buff that could be provided by several classes (Frost Mages, Ret Pallies, Survival Hunters, Shadow Priests, Destro Locks - learn it, live it, memorize it!). The tradeoff to opening up that mana return ability to multiple classes? You really needed to have it. Lots of folks didn't like this, as it went away from the BtPNtC attitude.
What do I mean when I say a certain buff is "required"? I use the word loosely. Shadow Priests were definitively required for Instructor Razuvious in 25 man, and that is certainly a different degree of requirement than Replenishment. However, there are certain buffs around which encounters and dungeons were designed. When Ulduar was designed, and when it was first released, it was done around the assumption that parties going in would have a Replenishment buff just as much as a typical tank/healer/dps setup. The same goes for Icecrown.
Blizz recently added Runescroll of Fortitude to the game, as well as Drums of Forgotten Kings and Drums of the Wild, admitting that they consider these buffs as somewhat "required" for raids (and therefore allowing you to have a slightly inferior version of the buffs without the particular class in your group) - i.e. the encounters are designed around the assumption you have that buff. Does that mean that you can't take down a boss without a Stamina, Kings, and Gift of the Wild buff? Not at all - it just means that you will have to work that much harder, or be geared just slightly better than the suggested iLvl.
Putting Diversification into Practice
When I first assembled the roster list for my babyicc10man group, I agonized over the buffs and whom to invite. Trust me, Fulguralis gave me hell for it. At the time, there were only 5 people in my guild, and therefore I had to reach out into my various networks to figure out the best way to fill out my group. I also had to consider the various group makeup requirements of each of the fights that had already been released when we started (I'm looking at you, Deathwhisper).
Prot Warrior - Tank
Prot Paladin - Tank
Disc Priest - Healer
Resto Druid - Healer
Elemental Shaman - Ranged DPS (designated Third Healer)
Arcane Mage - Ranged DPS
Affliction Warlock - Ranged DPS
BM Hunter - Ranged/Melee DPS (The Hunter may be ranged, but the pet is melee - for BM hunters, their pet is worth quite a bit of dps!)
Rogue - Melee DPS -> Later replaced with an Enhancement Shaman - Melee DPS
Retribution Paladin - Melee DPS
Since its conception, I had to change the raid night, and in doing so had some roster swaps. Having a second shaman made me cringe a bit, but in actuality, it has worked out marvelously. Besides, nothing wrong with have two sets of totems.
The value of this raid lies not just in the ability of each individual player, though I am insanely proud of them. I've watched the DPSers go from a struggling 4k when we first started, to pushing 7k on Festergut - and I know it's not just gear upgrades. The diversification scheme also helps a lot. They each contribute to one another's abilities. I base my personal gear choices around the assumption that I will have replenishment and blessing of kings. Even Fulguralis finally acquiesced that having a diverse mix of class combos also helps on the gear front (and trust me, he and I have argued about the raid mix question for months, so even a tiny acquiescence is like a gigantic victory for me!).
But it's not just about the individual buffs that each class brings to the table. Having a diverse group that covers every type of damage mechanic means that the same 10 people can go through the entirety of Icecrown Citadel without having to swap people out for certain fights. This was incredibly important to me - I wanted my group to be cohesive and comfortable with one another. If we kept swapping people in and out, we would constantly be battling the challenge of learning how a new player works. I could have simply ignored raid synergy, and brought only the highest DPS possible. I could have chosen only those with the best gear.
I chose not to do either of those things, because I wanted this group to go into ICC from the start, and grow as a group through the entirety of this raid sequence - together. Spending all the extra time and effort into building a solid and diverse mix of classes for the team from the beginning means that I don't have to worry later about whether or not we can take on a certain fight without our makeup - we can. We have multiple forms of rezzing, buffs, crowd control, healing, damage, you name it.