It's not unethical if it's an assistant that enables the user to live with greater comfort and ease. If it helps with recall and memory, with appointment-setting, with planning, or simply if it serves as a companion which suggests books and movies -- it's really the opposite of unethical.

What it shouldn't do is give specific advice on medical matters. Even if it's no worse than a doctor, or even better than a doctor, 9 times out of 10, that one exception could cause serious trouble. Unlike regular Chat-GTP users, people with dementia are already quite sick, are (usually) already on medication, and require more thoughtful care.

More importantly, it shouldn't be capable of mimicking a living or dead person. You'd probably need to hardwire it so that it has a name and "personality" of its own, which can't be changed by the user.