The reason the test and actually knowing who is likely to develop the disease is useful is that we don't know enough about the early pre-symptomatic stages of Alzheimer's. A lot of research has been focused on purging the plaques which form in the late stages of the disease and thus failed because these seem to be symptomatic rather than causative. The false positives are also very interesting from a research point of view because if someone is testing positive for the disease but it's not progressing this may give us a clue about how to control it.

The other slightly sad fact is that is also quite likely that any curative treatment will need to be started before you start to show symptoms, because the brain has already lost a lot of it's resilience by then.