Earlier quoted context omitted.
What is the point of generating a cryptographic key that you can never safely use?
I mean that the security profile of a simple 'locked box' that only knows the keys when all parties agree to unlock it is a very different from the security profile of a 'key distribution machine' like you described. I mean, if we all agreed to perform the decryption, the secret's out anyway. But not before then.
The real world use cases I most commonly support are things like CAs, TLS keys, financial transaction signing keys, and sensitive document decryption keys. All of these require single keys to exist that needs to perform automated operations, and needs to be on systems that can be backed up, restored, upgraded, and maintained, while able to prove no single person can access or control the keys.
The scheme I described can allow one key to be created, split, restored, used, and split again many times without full trust in any individual.