Historical, pre-digital precedent:
In the case of sudden death, there would not have been any way to securely dispose of any private "data". So your private information, diaries, works you purposefully didn't publish, unfinished manuscripts you abandoned - everything was handed down to your estate, and more often than not used against your intent.
I'm not entirely clear whether your will could specify such disposal to be done, or could prohibit people from at least publishing these private notes and letters if not reading them, in any kind of binding and permanent way.