Even if you avoid trusting the distributor, the quorum of share holders still will end up having to load a single key into a computer somewhere at some point to do cryptographic operations with it.

You need a trusted machine to do operations with the key, and if you are going to build that anyway then you might as well use it for generation and distribution too.

Well, now you've just turned your locked box into a key distribution machine, and there's a big difference in the security profile of each.

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.

Depends on use case I suppose. I can not think of many practical applications for one-time-use keys other than disaster recovery flows.

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.