I don't think there was ever a politically succesful Nietzsche-based regime,
Not directly but most of the most stupid concepts of the Nazis were drawn directly from Nietzsche and Hitler was a fan , even if Nietzsche probably would not have been impressed with him.
and Communism and Maoism have failed mainly because they were far too authoritarian and therefore self-contradictory for their own good.
Maybe you have not heard of the Dictatorship of the Proletariat. There was nothing self contradictory about their authoritarianism. They failed cause they were godless and poor economical understanding.
Atheism proper is quite the different beast.
Atheism proper is mere godlessness. But it is also interesting that however it outworks it usually fails.
The biological theory of evolution is almost as solid, albeit for entirely different reasons. You are lumping together very different things.
It is based on a materialistic naturalism and the theory has been accepted by most atheists with the exception of Nietzsche who had nothing to say about it and would have disagree that survival was more primary than power. The point was that most modern atheists are liberals and evolutionists. You would appear to agree with this since you mourn communist authoritarianism and celebrate evolution.
That is an entirely different can of worms, or rather two very different cans.
Personally I attribute it in Russia to the inevitable reaction to the repression against Orthodox Christianity, and in China to the ethically questionable proselitism of Christianity.
Also, I don't think it is fair nor enlightening to confuse Christianity with religion.
Nor is it at all clear what you mean by "viability of atheism".
The point is that everywhere that atheists take real control there is a systemic failure of society in the long run. In short atheism does not work - why should this conclusion differ whatever new form it takes.