So, as in the title. Why do they want them (more specifically black souls)? They don't need them to reanimate bodies, so what do they do with them? And how are Black Soul Gems created (seeing how Mannimarco was killed in Oblivion, so no more Revenant thingy)?

Soul cairn.
Summoned dead.
Necromancer.
souls.

1. Mannimarco is both a mortal necromancer and a god, as per the events of Daggerfall and the Warp in the West. The King of Worms may have been killed, but not the God of Worms. So, the Revenant "thingy" is still probably active. Besides, Azura's Star is corrupt when you first see it, and can be "fixed" to take black souls, too. So, there's ways around the Revenant thingy... just harder.

2. It's likely they use "black" souls as part of their necromatic rituals. Where do you think they animate ghosts from? Or how they enchant their equipment? Black Soulgems are wonderful to use for the budding Necromancer.

Also, why would anyone prefer Necromancy over Conjuration?

Probably because they despise living beings, but feel lonely at the same time. A soul is neither alive nor dead, it is perfect.

I've always thought necromancy is a discipline within the school of conjuration.

edit: nevermind, misread op's post.

Besides their obvious magical use, you can feed on them to extend your life span if you're going for lich status.

Relative risk-free Power.

Cavorting with Daedra is always risky, as the Daedra always attempt to play back. And the results can be... messy if they win. Read the book http://www.uesp.net/wiki/Skyrim:A_Tragedy_in_Black to see what I'm talking about. At least with necromancy, the things you summon aren't intellegent, and if there's a problem, it wouldn't be too hard for you to unsummon or kill the skeleton or zombie/dragur you animated. Usually. Unless you're stupid enough to animate something stronger than you while you're still an apprentence.

Souls go in soul gems.
They now become the Tamriel equivalent of a AA battery.

But what if you're powerful enough to summon an Undead army and you forget to ally it with yourself?

That falls under "stupid apprentence mistakes." I think necromancy tends to be one of those fields where it naturally weeds out those who are unfit to be necromancers.