I’m a little confused, are you suggesting that nihilism is a suitable reason for euthanasia?

If so, I think that is a misrepresentation of Nietzsche. The tldr version of nihilism, as I understand it, is that life is absent of objective meaning and all held values devaluate themselves over time, thus abandoning the idea that there is some objective perfection to attain also liberates an individual from the need of redemption from any god or government. The idea that improvement is necessary is something he compares to Platonic philosophy regarding a “true world” that operates invisibly in a state of perfection behind the visible world, and Nietzsche attributes this need to constitutionally weak people who can’t accept the human condition.

By contrast though, he does directly address the idea of suicide in the context of a noble conclusion of one’s life as being a positive:

“To die proudly when it is no longer possible to live proudly. Death freely chosen, death at the right time, brightly and cheerfully accomplished amid children and witnesses: then a real farewell is still possible, as the one who is taking leave is still there; also a real estimate of what one has achieved and what one has wished, drawing the sum of one’s life—all in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.” - Nietzsche, Twilight of the Idols

So we can extrapolate from these two viewpoints that suicide prompted from the idea that something can be improved by death is, at best, a misunderstanding, and at worst, a character flaw. On the other hand, suicide prompted by intention and a well founded justification that the body is no longer suitable for the purpose required of it, unburdened by belief of situational improvement, can be a legitimate exercise of the will to power.

So basically, nihilism isn’t equivalent to pessimism, but rather a liberation that is reached in a post-pessimistic state of being.

“Nihilism is best done by professionals.” ― Iggy Pop