There are more personal practical reasons too.

Even though it cannot be reversed or eradicated (yet, let's hope) detection can allow individuals to adopt interventions that help either adjust their lives to better cope with its progression or help mitigate some of the detrimental behavioral consequences. In addition, if you have family to care for it may be impetus to get certain things in order for them before later stages of the disease, etc. It's horrible and bleak, but I could certainly see why one might want to know.

In the lucky case, it can also relieve anxiety. Even though false negatives may still be possible, receiving a negative detection might give people who have anxiety about certain symptoms relief, since they can rule out (rightly or wrongly) a pretty severe disease.