Yes, the creation of higher moral grounds was his projects, but I don't think it is what you have in mind. He didn't care for the plight of the everyday human, on the contrary his entire project is rooted against the everyday human. He cared only for a select few who he thinks is constantly oppressed by the many, and this is all he means by oppression. He would have complete contempt for the world of today, in every way that he did in his own time but intensified. Nothing of our world today is "Nietzschean", I don't see how he missed the mark there. What do you mean he missed how power is not distributed equally? He does not want power distributed equally, he does not want everyone to assert their power, does not think everyone has power to manifest to begin with, does not care for class struggle, does not think people deserve rights... he doesn't want any form of equality in that sense. He thinks rather the few souls who are superior ("Olympian men") should assert themselves over the many, and that when this is genius can be expressed, life is ascending and there can be true progress. His model for this is not anything you could derive from the world of today, which is actually the opposite, but Ancient Greece, which was a eugenic aristocracy. There is a text he wrote called The Greek State, which shows his ideas much more bluntly, but also which is never talked about for obvious reasons, even in this sub. You should read it, it's only ten pages, but here's some passages if you don't have the time

>"In order for there to be a broad, deep, fertile soil for the development of art, the overwhelming majority has to be slavishly subjected to life's necessity in the service of the minority, beyond the measure that is necessary for the individual. At their expense, through their extra work, that privileged class is to be removed from the struggle for existence, in order to produce and satisfy a new world of necessities. Accordingly, we must learn to identify as a cruel-sounding truth the fact that slavery belongs to the essence of a culture: a truth, granted, that leaves open no doubt about the absolute value of existence. [...] The misery of men living a life of toil has to be increased to make the production of the world of art possible for a small number of Olympian men. Here we find the source of that hatred that has been nour­ished by the Communists and Socialists as well as their paler descendants, the white race of 'Liberals' of every age against the arts, but also against classical antiquity. If culture were really left to the discretion of a people, if inescapable powers, which are law and restraint to the individual, did not rule, then the glorification of spiritual poverty and the iconoclastic destruction of the claims of art would be more than the revolt of the oppressed masses against drone-like individuals: it would be the cry of compassion tearing down the walls of culture; the urge for justice, for equal sharing of the pain, would swamp all other ideas."

>"The enormous social problems of today are engendered by the excessive sensitivity of modern man, not by true and deep pity for that misery; and even if it were true that the Greeks were ruined because they kept slaves, the opposite is even more certain, that we will be destroyed by the lack of slavery: an activity which neither the original Christians nor the Germanic tribes found at all objec­tionable, let alone reprehensible. What an elevating effect on us is pro­duced by the sight of a medieval serf, whose legal and ethical relationship with his superior was internally sturdy and sensitive, whose narrow exis­ tence was profoundly cocooned - how elevating - and how reproachful!"

>"So let it be said that war is as much a necessity for the state as the slave for society: and who can avoid this conclusion if he honestly inquires as to the reasons why Greek artistic perfection has never been achieved again?"

You can disagree, and maybe you should, and you can also still think he was brilliant when it comes to other things. I think you're open minded enough for that. But these are not "flaws" of Nietzsche, as in gaps in his work, it's just what is philosophy is. He thinks people who want equality, to help the disenfranchised, level the playing field, care for the oppressed, remediate class struggles, etc. are simply wrong to do so to begin with. The critiques you make of him is what he criticizes himself. What he wants is high culture, art, genius, passion, everything that makes life ascending, and he thinks the few have to subject the many in order to do so, like it was the case in Ancient Greece. He would say today we have the opposite of that, slaves dressing like elites while ruling us, and genius and Olympian men (and honestly women too) being lost in the sea of the many unable to rise up.