I think there should be certain skills that can be put into one of two categories for example alchemy should be able to be in magic or stealth. Or another example Marksman should be in either combat or stealth. I think that would allow players to use options especially since alchemy is in stealth section.
Which category a skill is in really doesn't matter much anymore when you consider that classes no longer exist, it's pretty much just a method of classification.
I think putting alchemy into the stealth category was mostly a decision based on game balance more than anything. Bethesda wanted to keep the number of skills in each category even, and since magic already has the magic schools and enchanting, none of which would logically fit in another category, alchemy had to go elsewhere, or magic would have more skills than other categories, and when you get down to it, stealth seems to pretty much be the place where skills that don't fit in other categories end up, I mean, strictly speaking, speechcraft has nothing to do with stealth, but it's definitely not a combat or magic skill either. And I think that Bethesda said that each category has one crafting skill, alchemy for stealth, smithing for combat, and enchanting for magic, so from a gameplay standpoint, it really seems to me that making alchemy a stealth skill was the most logical option.
Besides, I've always found alchemy as a magic skill a bit strange too, because you're not actually doing any magic with it. Sure, you can say the effects of ingredients and potions are magic, but still, you're just mixing ingredients in such a way as to bring out the latent magical qualities in them, you don't actually use any magicka yourself. By comparison, the other magic spells mostly cover casting spells, and while enchanting doesn't involve any actual spells, you are binding trapped souls to items to give them magical properties, and while the exact proccess by which this functions is not explained in detail, to my knowledge, I think we can safely assume it involves use of some form of magic on the enchanter's part, so alchemy as a magic skill always came off as kind of odd to me. But I guess that's the problem with trying to categorize such a wide range of skills into three broad categories.
In any case, I doubt anyone would complain that it "doesn't make sense" if alchemy was a stealth skill from the start.
It also means we will get animations for alchemy. Like mixing potions and grinding up stuff with the mortar and pestle.We also have cooking too.
I wouldn't say it necessarily means that. After all, in Fallout 3 and New Vegas, you needed to find static objects for crafting, but you still didn't get animations for crafting items.
As to cooking, I'd assume it's just something you can do, not affected by any skills, as there aren't enough skills to allow for cooking to be a skill.