People with long term mental health problems suffer greatly with unbearable psychological pain. It is often as debilitating as any physical illness.
Suicide for these people maybe the only end to their suffering.
Without assistance people risk  permanent disablement or brain damage and also die in pain, if they are not helped in a safe environment with knowledgeable medical practitioners.
This should only be considered if

1) the person has been through long term or many shorter therapy without improvement

2) the person must have had some medications without any noticeable improvement taking into consideration debilitating side effects 

3) counselling should be provided to make sure that the person understands their decision is able to make such a final decision 

Assisted suicide allows people to prepare for their death, prepare those around them and importantly say goodbye to those they love.
Get their affairs in order and decide on what happens to their property. 
most important they will die with dignity quickly and not alone. They will not be at risk of perminant disablement with would be a risk if the patient calculates their doses wrong. They will die alone as having someone with them risks being prosecuted themselves. 

It also removes the trauma of someone finding the body as that will be dealt with and arranged before the death takes place.