"meaning, for example, that people with dementia could, while they are still competent, decide they want an assisted death at a later time."

This I have a problem with. Dementia,  currently, is unstoppable but in the future it may not only be stopped but a person may then be able to build new memories. You can never get the original person back but there may still be enough of the familiar left over to compensate.

That being said, a diagnosis of any form of dementia could be mind numbing enough that a person does not wish to wait and would prefer to end their life early and at their convenience. Waiting to do it when they become incompetent just seems the wrong way to go.

I hate to say it but the timing of one's demise should always be done whilst one is competent enough to throw the switch themselves.