Of course, they are both secondary professions, so maybe Blizzard believes that because they're more or less optional, you should be able to carry around all of your food and spices and lures in your regular bags. But cooking especially has gotten pretty complicated lately (there are a few foods that you've got to have in your bags regularly to do the daily quests, especially Chilled Meat), and so a lot of players would definitely find a use for a dedicated bag. First Aid, probably not, but Cooking and Fishing? Definitely.
And if you want to really dream, maybe food could actually get a bonus from being kept in a special "refridgerated" bag -- nothing big, just maybe a few extra points of the bonus stat or a little longer duration when you actually take care of your food rather than just tossing it in with all of the Kobold eyeballs and oily swords and cloth that you're also carrying around. But that would be extra -- for now, just a bigger bag meant for cooking and fishing utensils would be fine, thanks.