It all depends on the key wrapping used. Key wrapping is little more than encryption of a key with another key. Although key wrapping schemes certainly exist (and are considered rather secure in general) other key schemes may use common methods of encryption, both symmetric and asymmetric. And in the end, how strong the encryption is depends on the method used.
I've seen AES keys being encrypted using AES-CBC, which is perfectly fine for AES-128 and AES-256 keys. Wrapping an AES-192 key that way could already make it vulnerable padding oracle attacks. Encrypting a structured RSA key using CBC and an IV of zero bytes (as used by many HSM's) may even passively leak information to adversaries.
Encryption itself is already a chicken egg problem. You've got this data you want to keep confidential. Now you can encrypt it, but you'd need to secure the key now.
So why is encryption or wrapping useful? Well, not all keys have the same properties. Some keys such as public key for asymmetric systems can be distributed using a public key infrastructure, but they can perfectly use to wrap AES keys to perform key establishment. Other keys are distributed in advance, taking advantage of the moment in time that the key can be established. Yet others take advantage of hardware protection in HSMs or smart cards. So key wrapping is an important tool to perform key management. Note that one wrapping key can be used to wrap many other keys.
As for your examples: yes, a key can be transported over TLS. However, TLS is point to point transport security. After TLS is stripped you'd just have the key. It is much more secure to wrap the key and provide end-to-end security. With a bit of luck the key may be unwrapped directly within a HSM and never even appear in memory. Note that earlier forms of TLS, the TLS_RSA ciphersuites, actually perform a form of key wrapping to establish the master secret to derive the session keys from.
A password protected store can be used. Often the keys in those key stored can be protected separately as well. PKCS#8 could be seen as a high level form of key wrapping, for instance.
However, such key stores are not always useful. For instance, you may want to wrap a key in a HSM to sync it with another HSM. In that case you'll need a wrapping key in both devices. Generally HSM's cannot simply create a password protected key store for that.
Similarly, a device can offload wrapped keys if the memory is limited. This is a common method within TPM modules in PC's: instead of having a high end smart card chip, keys are wrapped with a TPM specific key and stored on the system's drive. When they are needed they are simply put back and used. This way the keys can be secure both at rest and when in use, even though they are not stored in the hardware device.
Wrapping / unwrapping a single symmetric key with another symmetric key that has the same access level probably doesn't make too much sense. But for key management key wrapping is a very important - if not essential - tool.