Gear is one of the main things holding back the idea of a "hybrid" role in a raid, so I can't see it being factored out. T4/5 comes in a few different flavors, but none of them really let you do two things at once very well. The only exception seems to be Feral (spec-wise as well), and most bear tanks I've talked to weren't too thrilled with their T4.
If you could change gear in mid-fight, sure... But right now it's only possible to change effective roles from one battle to the next, and even then it works out better to figure out which role comes up more often or importantly, and spec primarily for that. There are little exceptions -- a prot paladin can take Spiritual Focus and heal uninterrupted, but he can't take SoC and expect to do any sort of serious damage to a mob being tanked by someone else.

This is because in the run-up to 1.9 there were a bunch of people on the paladin forum making loud noises about wanting to be able to specialize. The developers unfortunately have a habit of listening to the wrong people at the wrong times, and the result was a lot of decisions like moving Spiritual Focus a tier deeper in Holy, which forces a tank-healer hybrid class to "specialize" just to be able to heal while under attack.

Just to clarify, what exactly are we talking about?

1) Utilitizing multiple roles in one fight?
or
2) Utilizing multiple in a raid split between different fights?

To 1)
Obviously only works well with roles that have play style/gear overlap such as damage casters and healing casters or tanking melee and DPSing melee. If you try to start healing in your full feral gear, you won't get many heals off before you go OOM. Likewise you won't stand a chance if you try to tank a raid boss in your Resto gear.

To 2)
This is basically an extension of 1) with the difference that you can swap gear now. The same combos as in 1) will still work here. Balance and Resto give OKish synergy to work. Feral until HotW works OK for Resto as well I guess although it is way inferior to Moonglow for healing purposes. Resto gives utility in the first 3 tiers. Any higher and it offers you jack for non-healing purposes.

If I was going to spec some sort of Hybrid, I'd go with the first 3 Resto Tiers as basis, then go from there. Feral gives you the melee Hybrid aspect, Balance the ranged caster DPS aspect with better Healing. Here is what you have to decide. Speccing into all 3 trees is, in all honesty, stupid (not counting the 11 points in Feral for FC a Balance/Resto might pick up for PvP). I am not too good with creating Hybrid specs for level 70, so I'll leave it at that but the old well known Melee/Healer hybrid is a variation of 0/30/21 (HotW+NS).
[list=1]
Back in the day when I was a fresh level 60 Druid with Balance spec I joined an LBRS 10 man PuG. I ended up tanking with zero points in Feral because the only Warrior in the group happened to be that type of Warrior that would hold his Sword with the sharp end and swing at mobs with the blunt side if the game didn't forbid it. Well anyways, we got to the Ogre boss you have to summon and the main healer happened to die. I stunned the mob I was tanking (I think it even was the real boss mob) and CRed the healer and resumed tanking. We managed to kill the boss and I was like "Wow, what awesome hybridity!".
</Old Geezer voice>

But in hindsight I have realized two things:

1) This doesn't work with bosses that cannot be stunned or hit hard (my Feral gear was pretty crappy at that time).
2) This is not being a Hybrid. Any Druid spec could have done the same I did. Bash and CR are trainer learnt after all.

Regardless, there are still times I love the different roles of my Druid - but it's a shame I have to do 5 mans or have to duo Scholo to be able to see it because of how the end game raids work.

I sometimes do get the impression Druids are 3 classes that share one name. Just take the Druid forums as example: You'll find a battle royal between Balance VS Feral VS Resto Druids in nearly all posts. Balance will tell everyone that he is the best for PvP, Resto will tell every "off spec" to L2P and that Healing is the true way of the Druid. Then there are the Ferals who will claim that shapeshifting is our role, and that Ferals are the real Druids (add some: "I have been Feral pre 1.8" emo here). I am not sure if I am supposed to be proud or ashamed of this.
On one hand, having so many play styles will obviously cause animosity between the different specs and you could argue this is a good thing because it indicates that Blizzard succeeded in creating a multi role character.
On the other hand, I am ashamed to see posts such as "Ok, nerf Feral because Balance is inferior!". I mean, do those people forget they are still one class and that every buff/nerf to any tree is a direct buff/nerf to them, too?

I am sure you can find this behaviour in nearly every class forums; even the Warriors who are reluctant to admit being hybrids have their own DPS/Tank-only trolls.

Just to add another thing to the discussion:

Paladins (and Shamans I guess, but I only have experience with Paladins) are better suited to play Hybridish in most cases. Paladins use their mana to tank, DPS and heal after all so the gear overlaps alot more than that of a Feral Druid trying to heal (low mana pool plus added mana cost to shift back into forms although I am not sure how the new T4/T5 Feral set works with that).
This alone should make a Paladin wanted for raids IMO.

Their buffs alone would make Paladins wanted already, even if they wouldn't do anything else ;)
Paladins are very well suited to fill in more than one role, because they get a lot of abilities of all roles as core abilities, and don't need to spend many points to fill in one role okish and can concentrate on one other role to shine in. The gear also supports this. My experience with Shamans is limited, but as far as I gathered they don't have it as easy to fill more roles, because they have to invest a lot of points to really make a tree/role worthwhile. Druids fall somewhere in the middle ground, having their forms and heals and damage spells as core abilities, but them being only mediocre without the talents to support them. Their playstyle is also far more "fractured" if I may say so, they can switch the role very quickly, but not act in several roles at the same time.

Personally I think Paladins are the only ones who could justify a true x/y/z spec in endgame raids (and count as Hybrids), while Druids, Shamans (and Priests) would need to invest far too many points to make all aspects worthwhile, forcing them to concentrate on one role. Shadow Priests, Enhancement Shamans, Feral Druids in raid? I can imagine it easily, yes, but Shadow/Healing Priests, Enhancement/Healing Shamans, Feral/Resto Druids? Unlikely if the gear isn't specifically designed to counter the lack of talents (making it worth far more than the ilevel would allow).

There are only a couple of hybrid specs that work out okay that I can see. A druid with 11 in feral can be a decent enough offtank and can hold aggro on something that's not being dps'd hard from the get go. A shaman with 11 points in enhancement can at least swing a big 2 hander and do some more damage while still being able to drop totems, heal, shock and the like.

Most other specs require a heavy investment. While I don't know about Paladins, an elemental shaman isn't very powerful without lightning mastery which means you're spending 30 points in the tree. A priest won't do a whole lot of damage without shadowform, and won't have much utility unless you get shadow weaving, misery, and vampiric embrace and maybe silence, all of which require a fairly steep investment. A druid without mangle (or at least shredding attacks while grouped with a mangling druid) won't do much damage at all.

This isn't really a problem per se since you need to sacrifice other talents in order to get that kind of power, but most "hybrid" specs just aren't very effective

Shadow priests are acceptable dps only because of the Base*coefficient*1.15 *1.10*1.15*1.05 and arguably a last *1.10, but we don't control curse of shadows =P

*1.15 -20 point investment in the tree
*1.10 -30 point investment in the tree
*1.15 -31 point investment in the tree
*1.05 -40 point investment in the tree

You're losing 32.25% by only going in 20 points for a pure hybrid build, and by the time you get to 30 points, you might as well hit the 31st and put a hole in hopes of pure hybridization. Once you've given up hope of a 21 point talent, the pickings are slim enough to make Misery a respectable alternative. Once you have misery it's pretty much a crime not to take VT for raid dps.

It culminates in a very solid dps package at full investment, but partial investment just doesn't create the kind of returns you'd expect for the sacrifices you have to make in the healing trees.

In short a partial shadow priest is pretty much just a shadow of the full strength capabilities. You're far far better off speccing holy dps and filling it out with whatever healing talents you can grab for cheap on the way up. You sacrifice all the raid based goodies that make shadow priests attractive though for mediocre dps and mediocre healing (if you're true to 50/50 dps healing).

It is a hybrid of sorts.... but when's the last time someone asked for more smites on the boss? Seriously =(

Well, I could see a Paladin with just enough in Prot to improve Righteous Fury being capable of keeping aggro on mobs when needed, similar to a druid with a small Feral investment. As a healer, he'll have a shield on anyway, and a ranged taunt is invaluable for picking up loose/deaggroing mobs.

Way back when, not long after I hit 60, I tried a hybrid priest spec. It was a little better with the old trees, healing wasn't gimped quite so badly with it. But as Bekah points out, Mindflay is very weak without all those multipliers. This came home to me when the newly released damage meters showed a wand spec priest beating me while dragging someone's alts through ZF. Now granted, I sucked back then and he had a nice wand but still, wands?

Not too many months later, secure in my old style Disc/Holy build, I was doing something with another 'Hybrid' priest and was happily out DPSing them with Smite. Now this was the old and slow Smite and I didn't have much, if any damage gear at the time.

Blizzard's talent revisions certainly have made classes more specialized. I get the feeling they didn't want people to do stuff like 31/30 builds and intentionally set out to avoid some of the most powerful ones, either by putting shiny, must have talents 41 points deep or by rearranging talents.

I've done a Tri-spec twice, once going all the way to silence, and the other just to mindflay (oh why can't Mindflay be trainable).
And each time I never thought my mindflay would be great damage (although extended SW:P was nice).

To me it was mostly about having the slowing proc, and additional chances to proc blackout.
Which worked well for me while I was pvp'ing a lot. Great for slowing/stopping a flag carrier.

I ran with a 19/11/21 spec while doing the PvP grind on my druid back around patch 1.10. It's an amazingly useful PvP Hybrid spec, which means it fails horribly with raiding. I was still a decent healer, always top 50%, but that's more of a statement of my gear and skill than the spec. I was best off wearing warlord gear and switching from nuking to catform once oom if I wanted to do DPS, and Tanking was pretty much right out.