Well, for the starters, when you craft something, it's almost always better than anything you will get from the NPC/monster drops.
Later in the game, there are special equips that can only be crafted, so that means you will have to entrust the crafting process to someone else.
Also, should you decide to level the crafting skills later in the game, you will regret it. While it's still possible to get "natural" ingredients like wood or iron, the droprate of all monster drops decreases if you are some levels above the monster level - the higher level you get the harder for you will be to level up your crafting skills.
If you are playing multiple characters, you could concentrate on leveling the crafter skills of only one, that would make it easier/faster, since you will be getting 2x items and only using them on 1 set of skills.