You provided a scenario where the mental illness hampers their ability to be an adult. Those with a mental illness that doesn't hamper their ability are necessarily excluded from that categorization.

Lack of capacity is narrowly defined. So, a person may be able to make decisions about who they have sex with, but not able to look after their finances.

But some of those mental illness are treatable (depression, OCD, etc.) and the individual can get back to `functional' once `treated'. But in the crux of the battle against the illness they are not able to function properly: should they temporary be unlabeled ? (I think so, but what does it imply regarding responsibilities ? How can one be responsible for his healing if the very disease they have make them not seek relief ?).

I believe labels come and go according to circumstances.