The problem about everything incurable is that it's currently incurable.
Take a 30-year-old who would qualify for euthanasia (if your answer to the question is yes). It's not unrealistic that in some twenty years scientific discoveries could be made about brain chemistry or whatever that could provide them if not normal, at least acceptable life for decades.
Right to die is usually accepted for situations where death is already inevitably on the way and it's just about right to a better death.
Here we are talking about a more general right to choose death.
With mental illness there's a Catch-22 about euthanasia: if one has so severe condition that it would justify right to die, then surely they are not capable of making such decision themselves. And while there are obviously situations where someone else has to decide to pull the plug, you can't euthanize someone without their own valid agreement.