My personal top PvE team was:
- Pally (Tank).
- Demo Warlock (DPS, +SP Buff).
- 3x Elem. Shaman (DPS & Heals).

One of the shammies was dual-spec'd to Resto.
But I almost never needed the extra heals.

I like having a dual-spec healer.
Because when you don't need the healing, they can go damage spec and help you clear things faster.
3x Shaman, can heal as effectively as 1x Healer in a Healing spec... but they put out a lot more DPS to clear trash faster too.

A dedicated healer now gets you a Magic removal, from Holy/Resto tree, that DPS casters do not get.

More classes, get you additional crowd control options.
Mages can Polymorph.
Priests can Shackle Undead.
Warlocks can Banish Demons/Elementals.

The Paladin and the Druid... are much easier to macro, and tank without a lot of your attention.
A Warrior or DK can tank as effectively, but will take a much larger portion of your attention to do so.

Druids and Priests are very mobile healers.
Shamans slightly less so, and Paladins are very much a stand still healer.

Additional classes is more buffs.
Not everything stacks, but some things are exclusive.
Paladin/Druid brings King/MotW, Paladin also brings Might.
Priest brings Fortitude.
Warlock brings Imp stamina or Felhound intellect.
Mage brings Brilliance.

Not every buff is a cast, with an icon.
A boomkin adds +spell power to their team through straight DPS.
A warlock does the same, via a curse.

A mixed team means... you're more likely to be able to use every drop.
But an enchanter on the team means things that aren't useful to you, at least get you maximum value (vendor price or enchanting mats price).