neitschze from what i understand hoped that with the decay of religious institution people would implement their own morals structures instead of having to rely on religion or stuff like communism etc, this was his idea of the ubermensch who would be a self sufficient spirit with no need for external institution
the survival of the fittest thing just came after the nazis twisted everything he said to suit their racialist aryan centeted ideology, i dont think nritschze cared for that at all, he also said that all anti semites should be shot and stuff so he was probably against it as well
True, the end goal is for all of humanity to become übermensch, but the concept of it implies that a single individual has the right to act selfishly if they're powerful enough to create their own morality. They're not to be bound by the limitations of others.