Also, a "pure mage" player that never used or trained non mage skills could never make use of half the products of alchemy : the poisons were useless for mage staves.
A mage, or any character type would reap the same rewards from potions and poisons. That's part of the beauty of it. It contains powers for all play types.
There are many polls on weapons and character types, I think you will find the dagger or something else as the most common weapon used by mages.You WILL use other skills beside the 7 mage skills. It's just the way characters leveled in TES games, not blocking would be stupid. Not running to get somewhere faster would be stupid. Magecraft is based around intelligence. Being a pure mage by your definition would be impossible, or very difficult. imo not actually how the devs thought was going to be the most common play style, well the vanilla game mechanics sure don't encourage it. Thus it's not popular in the player base, and basically the mechanics were as such that it didn't matter much if you were a Warrior/Thief?Mage for anything.
So even when redesigning the system, I do not see the logic in taking a very thin slice of the mage playing populace and apply that kind of obscure against the grain play style to the much larger player base. And then use that to justify Alchemy being a Thief skill
Staves were not even considered melee weapons, why would they benefit from poisons.There weren't many good staves in oblivion anyway, and are pretty much gimped imo. I don't think they were that popular with mages, secondary weapons only. I really hope they make them useful this time. Melee damage and ability to use a poison would only be a start. I think they are coming up for a big overhaul.
Further more, by your logic: It shouldn't be a mage skill because playing as pure mage(which is a rare play style), means only using a staff as a weapon(which wasn't a common primary weapon), so can not make use of half of what alchemy has to offer/ But Thief classes can, thus it is Stealth/Thief skill. It could just as well be a Warrior skill in that case, as they can make full use of all the benefits as well. The extra buffing and extra damage from poisons, Alchemy is a perfect match to a most warrior play styles.