It's because Stealth is more than just a thief. Alchemy is a science, it is like chemistry for cavemen. There is nothing mystical about it, a poisonous mushroom is not 'enchanted' it is just venomous. A thief may use alchemy for invisibility, or nighteye, or chameleon, or speed, or acrobatics, or health, or magicka if it is a mage/thief hybrid. An assassin would use it for all of these and poisons like Paralysis, damage health, etc. A mage would almost never fight hand to hand so it would only need potions for restoring magicka and health.
When it boils down to it look at Oblivion. What character was most likely to make a bunch of potions? A mage, because it was a magic school. Would he use a fortify blade potion? No as he casts spells. Would he use a poison? No, he casts spells. Who uses most of the potions that can be made? A stealthy character.
The same thing happened in real life history. Those who were once hailed as witches with magical potions resurfaced as doctors with medicine. The world of Nirn merely evolved intellectually, and sees Alchemy as a science, not an art.
No offense but I disagree
When I have a mage they rely on alchemy enormously
1. I use it for an important money source early in the game - my mages are not thieves so make their cash via making and selling potions
2. My mages have minimal strength - they can't carry much on their own, in order to control levelling up too fast I avoid feather spells and prefer feather potions
3. As an intelligence skill Alchemy is very important to my mage for improving my available magicka pool
4. In previous TES games alchemy allowed me to ensure I would get the maximum bonus for the level
5. My Mage would depend on carrying home brewed health and restore magicka potions for successful fights - this will be even more important in Skyrim seeing as I can't run backwards fast in combat anymore, my mage will need alchemy more than before to stay on top of things
I'm not sure I see Alchemy as a science - probably due to all the fantasy ingredients and effects - most references to alchemy call it a pseudo-science due to it's focus on transmutation or achieving the elixir of life and while I understand the use of poisons for stealth characters I still feel it is a more appropiate skill for mages