I would generally assume that you are able to create items for your specialization. You don't necessarily need a crafting specialization for that. A crafting specialization lets you do more than you would be able to do, more powerful items, more uses, etc.
If you don't like that, you can easily re-frame how focus and enchanted items work for your character. Look at Harry's pentacle, for example. It's a focus item for him, but he didn't really build it to enhance his magic, it's just an item that has a lot of personal value for him and that's hoe it enhances his magic. The same could be true for your character. He didn't store a spell inside an enchanted item, the item just helps him do a spell. The enchanted item is just the way you express it on the mechanical side.