It's the Mages Guild that created arbitrary categories to magic, mainly for beginners to ease its understanding. In reality, all magic is related, and a master of magic knows this and are able to break the barriers and such petty categories.
How would you explain being able to "level up" arbitrary categories, potentially mastering one while still being a novice in another?
In Morrowind, Soul Trap, Demoralize, and Telekinesis were all part of the Mysticism category, as you put it. Becoming more proficient in that category meant you were able to use more powerful versions of each of those spells. However, all three spells are now part of three different schools of magic in Skyrim (Soul Trap in Conjuration, Demoralize in Illusion, and Telekinesis in Alteration) -- becoming better with one doesn't affect the others at all.
The schools obviously play a larger role than you're giving them credit for (in a single game, at least), and yet Bethesda seems to value them differently with each new game. That, to me, shows a lack of both understanding and willpower to conform to the lore they created for the sake of making things easier on their part.