The documents with no company to hide behind. A diagnosis, a divorce, a family dispute, tax and investment papers, a will: these are the most sensitive documents you own. There is no employer's compliance department between them and a cloud API. On a machine in your house, the file never leaves the room. There is no copy at a provider to be subpoenaed, leaked in someone else's breach or used to train someone else's model.
A household, a family office, or staff who help you. The moment your assistant, accountant or a family member has to work on the same confidential file, “just don't use AI for this” stops being practical. A machine you own is the only version where all of them can work on it and no third party ever holds the material.
A machine like this is not cheap. As a private individual, you do not buy it to save money — you buy it so the most sensitive papers in your life are never on anyone else's computer.