If you let an animal die like this, it would be called animal cruelty. I'm happy we have the option here in The Netherlands for a less painful and dignified death.
I would also prefer the option of assisted suicide, but hospice is a reasonable option.
Hospice doctors and nurses are trained in palliative medicine, and the hospices themselves are peaceful places, very different then hospitals. I have unfortunately spent significant time at two hospices this year, and had an old friend choose hospice care at home. It was a very humane way to go, with no suffering.
I think self-euthenasia should be allowed, but letting nature take its course has a certain clarity to it. Especially in cases like these, where disease progression impairs decision-making faculties.