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"Sure, some of them would do so. But then what degree of pain and suffering should qualify?"
I dunno. Maybe the person's who dying of cancer?
Where do you draw the line? Terminally ill patients suffer for months or years living a less then desirable life and would jump at the chance of being able to leave painlessly and peacefully. 

Sure, some of them would do so. But then what degree of pain and suffering should qualify? How to set a standard? Cause we are to enable legally killing a person and that understandably should not be easy.

I don't see a problem with this as long as family members agree that is the best procedure to follow for the person.

Why family members? We have two problems here - both possibility of family members needlessly prolonging suffering in cases where assisted suicide is wanted by the patients and possibility of family bullying a patient into suicidal thoughts to warrant an assisted suicide.
And what about medical malpractice? There are absolutely horrible people who shouldn't be doctors, who can use it to make statistics of their hospital look better. On the other hand we will have doctors who are devoted to saving lives who will be forced to kill people.

On the other hand I also see those with severe mental health disorders.

That is a complete different can of worms, introducing eugenics. People with severe mental disorders often are not able to decide about themselves and we are discussing the topic of deciding should they live or die. Don't you see an obvious danger there?

So why do we allow people to suffer? 

Because ways to resolve it are very likely to introduce even more suffering. That is the sad truth. We are pushing the boundaries of medicine to save or resolve issues with many health problems, but there will be people who are beyond saving as of now. But would they be beyond saving tomorrow?
How are we to study those diseases and try new treatments if we decide that they can die? How would a family feel if they decided to let their family member die to ease suffering if two years later there is a breakthrough that allows to cure their aliment, or make it bearable to live with it?