I wouldn't say I'm very well-versed in cryptography. The reason they're separated is that it allows you to:

  * Further split up the trust such that the key shards can be held by one group but they don't have access to the document (maybe you keep a copy of the document with a lawyer but distribute the keys among your friends and family so that if your lawyer is hacked or bribed they can't reveal the secrets, same goes for if your friends conspire against you).
  * Make the shards small, independent of the document size, so that they're always practical for friends to store even if you have a very large document to save.
  * You can do a quorum expansion (create new shards that are compatible with the existing shards) without revealing the secret.

To be fair, for practical uses this is not super necessary but it adds flexibility without losing anything in return (I would argue the quorum expansion point is actually a useful feature).