Alteration with such customization would be great. I support that all the way.
As for open necromancy? I don't think there should be a school, no. It goes against the very nature and spirit of necromancy in the first place. It's supposed to be an underground school of thought, one that's taught behind closed doors between allies that's completely taboo. Having a "school" would make it feel official or - hell - like the dark side of Hogwarts or something. Instead, I'd rather see more detail and depth added to the exploration of necromancy as seen in Morrowind and Oblivion. With the tombs of Skyrim, necromancy would be a serious issue. I feel it'd be far more interesting to explore it in a similar fashion to how it's been already explored.
I think there's a language barrier here. In English, School has two connotations. The one it appears you are thinking of is an organized instution of learning. The other is simply a body of knowledge, philosophy, or thought, which one or more people knows.
So, for example, in TES, each of the different 'disciplines' of magic - Restoration, Alteration, Destruction, is a "school" in the second sense. What the OP is suggesting is adding a new list of spells, basically, which would be categorized by a "Necromancy" skill/school of magic. It has nothing to do with an 'organization' in this case.
The flip side of that is, if you joined a necromantic cult, and they teach you necromancy, are they not acting as a 'school' for their disciples, in the sense of an organized institution of learning - a 'school' doesn't have to be a public, state sanctioned institution to be any less a school.
However, the main meaning in this discussion has nothing to do with institutions, and everything to do with a body of knowledge related to that type of magic, and more specifically, an in-game set of magical effects related to necromancy, and an associated skill..