Why is it a bad idea to use a UTF-8 derived symmetric key? Given a cryptographically secure series of octets, it is often useful to display this information or store it in a database in a textual format such as hexadecimal.

Why would it be incorrect to take this hexadecimal and encode it with UTF-8 to derive a symmetric key rather than converting from hexadecimal back to the original byte array?

My thought is that it reduces the key space and presents a bias toward where hexadecimal characters fall in the UTF-8 encoding scheme. Perhaps someone can clarify this for me.
The strength of a symmetric key is determined by the amount of entropy. In that sense your scheme would not increase or decrease the security by much. However, you would be specifying a higher key size than actually used. For instance your AES-256 bit key would have the same entropy as an AES-128 bit one. You'd use a slightly different key schedule and number of rounds as well of course.

Besides that you may run into problems when somebody decides to use a different encoding (hex encoding in UTF-8 is the same as just using ASCII though) or a byte order mark. It could also be possible to mix up uppercase and lowercase characters.

In the end you're only fooling yourself and possibly others if you'd use this kind of scheme. It is very bad practice. If you have to store the key as hexadecimals then pretty please with sugar on top, convert it back to the original form.

In general though you should never ever have to store a key in a string in the first place. Note that strings may be very hard to delete from memory. Instead store them in a key store such as PKCS#12 or preferably in a hardware device.