As I pointed out earlier, mental illness is treatable.
In all cases all of the time, or in only some cases some of the time?
While I fully accept that current treatments are not perfect, they can work for many, so offering such people an easy-option of suicide does not seem like a good idea.
What do you propose to do with the not-many?
Secondly, (as has been mentioned) those who are physically fit do not need any assistance to kill themselves.
Those who desperately need an option of euthanasia are those who are facing a slow painful/humiliating death but are physically incapable of taking action themselves or travelling to an overseas facility.
Perhaps it has a lot to do with the fact that killing people medically (typically via a large dose of barbiturates) is easy, quick, painless, dignified and certain whereas typical suicide methods (depending on specific method) are none of these.
You wish to die. You can either throw yourself beneath a train, with all that that entails for trauma to the driver, the team needed to scrape up the bits, delay and disruption etc., or you can fall asleep in bed and never wake up. Your call.