I agree that Nietzsche is important to the atheist-theist debate and that contemporary “new atheists” tend to ignore him, but it should be remembered that Nietzsche never made any direct case against theist arguments, but instead went straight to the consequences of rejecting them (which he tried to bravely face and work out under the assumption that God does not exist).
Theists generally think Nietzsche failed in his effort to overcome nihilism, and so they obviously want to bring focus on Nietzsche so that contemporary atheists don’t squirm around the consequences of their atheism.
But theists have also had over two millenia to home in on and refine their arguments for the biblical God’s existence. The theist philosophers promoting God’s existence have also had over two millenia to make a somewhat subtler case. The fact is that both theist projects have largely failed. Neither the God of Bible believers nor the God of theist philosophers is especially convincing to those with enough education and intellect to follow the arguments made for them.
What this means is that if you have a need to believe in God as understood by the monotheistic religions or by theist philosophers, you’ll rationalize your way to that belief, and if you don’t have a particular need for God belief, there’s nothing compelling in the arguments for God that are likely to draw you away from agnosticism or atheism.
I wish the case was better for God’s existence. But the truth is that we live in a cosmos of flux and death that does not speak to us as to why these things are so. We’re all guessing, but very few can bear doubt and agnosticism, so most take sides (ignoring the problems of the side we take).
A nice dose of Socratic humility before the ontological mystery would suit us better. But the reality is that our positions on God are part of our immortality projects (whether symbolic, such as writing a book for future generations, or literal, such as praying we’ll go to heaven), which are in turn connected to the groups that give us self-esteem and provide us with love and affirmations of meaning. So we’re emotionally and intellectually locked in against those outside of our group and can’t admit the obvious: that we don’t really know what or where or why (if there is a why) we ultimately are.
Whatever we think we know, there’s a lot more that we don’t. We only know what we know. But we do not know how much we do not know. And what we do not know might change the character of the known if it should ever become known.
The next time you find yourself expressing a great deal of confidence on a matter of religion or irreligion, that’s something to bring to mind, with or without Nietzsche or Socrates.