I may have been a bit rash to say, "there are no problems that adding scrypt solves," but whether you need a KDF for encryption is more of a practical problem. There are many circumstances where it makes sense, but I'd consider that a part of your password policy. In general, encryption is secure by itself, and I'd avoid adding unneeded steps.

As for password hashing, that is a very different application than deriving a key for encryption. You are storing the result (usually in a database), and in the case there is a leak, hoping that no one can brute-force the passwords. This is when you start the process of changing salts and work values (in the case of scrypt), and getting everyone to change their password. Using a KDF in this case makes a lot of sense.