After a couple of months of play even seasoned noobs like myself know the general guidelines of what to bring to a raid.
You know that the standard composition for a 5-man is 1 tank, 1 healer and 3 DPS.
You also know that this scales fairly well into 2 tanks, 2-3 healers and 5-6 DPS for 10 man raids and this scaling continues into the 25 mans with 4ish tanks 6ish healers and 15ish dps.
By now we also know that it is preferable to have min-maxed or so called pure specs for whatever the highest level of content is that you're running. This is based on the fact that min-maxing optimizes use of talents, gear and skill for specific tasks meaning that a 'pure' tank will be better equipped to tank than an off-spec tank (and I use this term with care).
This is beyond argument by now. We've seen the math. We know that someone who will dump all his talents into the protection tree will be significantly better at tanking than someone who doesn't, we know that a full holy build will outheal a shadow priest by a margin. This is not to say you can't get the job done with an off-spec; It's to say that a 'pure' class will simply outperform an off-spec in the same role.
But where does the hybrid fit in with all this then? When does the versatility of having '2' specs bring more to the table than being 100% invested in a single spec?
The answer is simply: Group Size
No group is perfect, things do go wrong so lets take a look what happens when groups start falling apart:
25 - mans
The main tank dies, the boss makes a b-line for the nearest healer and smushes him/her before the off-tank can pick things up. The group is down a healer and a tank but the remaining tanks/healers should be able to hold things together without too much trouble. The raid risks going out of mana sooner and DPS may have to pause for a while becoming useless for that period but things are very much saveable.
Having a hybrid tank or hybrid healer in this situation isn't going to add much. A little extra healing from a DPS / healer hybrid will help preserve some mana but this would cut into the damage output and prolong the battle making the net result 0.
If another tank and healer die you're most likely looking at a wipe unless you have multiple hybrid DPS / healers standing around capable of switching roles.
Be that as it may a hybrid in this scenario would add very little to the overall raid.
10 - mans
Once again a tank slips up or the healer accidentally draws aggro, both main healer and main tank go down leaving the raid with 1 active tank and 1 or 2 active healers. In this case there's a lot of pressure on the off-tank who now has to deal with both the boss and adds or just the boss and let the adds roam free.
Healers will feel the increase in strain from 1 healer going down as well as having to deal with the extra healing needed on the off-tank or worse having to heal DPS who are essentially sitting ducks to any free-roaming adds.
A hybrid DPS / tank could have a significant benefit at this point by picking up stray adds. A hybrid DPS / healer could ease the strain on the remaining healers by picking up a raid healing role.
5 - mans
A potential worst case scenario in a 5-man run is always the tank and the healer biting the dust leaving 3 dps exposed, fighting for their lives and resulting in a wipe 90% of the time.
By swapping out 2 of the 3 dps for hybrids like a DPS / Healer and and DPS / tank means that even though the group is now severely weakened it lacks none of the components of a succesful group. The hybrid tank is tasked to pick up the mobs, the hybrid healer can switch to healing from DPS and the DPS can continue to DPS turning a potential full wipe into a potentially stable situation.
1 - man
Lets not kid ourselves. We are alone most of the time when questing / doing dailies or soloing various azeroth content for a friend (i.e. boosting). If you cannot tank the mobs of kill them faster than they kill you, you lose time. Precious time you spend corpse running. If you're a pure tanking or healing class you are simply trying to outlast things and if you're a pure DPS class you better hope that enemy dies before it comes too close (a generalization but you get what I mean).
A hybrid doesn't have these problems. Both the hybrid DPS / Tank and the DPS / healer have excellent survivability solo coupled with the ability to do at least a decent amount of damage.
When looking at hybrid's it's important to realize that a hybrid is not something that plays 2 specs at the same time but something that can smoothly switch from one spec into the other.
If you are a DPS / Healer your primary role for any group will be DPS, picking up healing in case of emergency. You are not there to do both. You should not feel obligated to throw heals as a DPS / healer hybrid if you're there to dps and things are going fine. You are there to pick up the slack with your 'secondary' tree if it is needed.
Your role is to keep going when others can't. If your DPS has to stop because of aggro issues your hybrid can continue to perform by throwing a few heals around or off-tanking a stray add.
Group size should be the determining factor for any raid leader or group leader that is putting together a group. In general terms the larger the group the smaller the need for a hybrid and the less utility a hybrid will bring to the table. However the smaller the group gets the more utility a hybrid will bring to the table in case of emergency... and lets face it: shit happens.
A hybrid should not strive to top the damage or healing charts. It should strive to do what is needed to keep the group up and running no matter who gets the credit for best healing performance or best damage.