Avengers: Age of Ultron is about how this is actually a terrible idea. Part of what makes the Avengers franchise popular is that it gives depth to superheroes and portrays them as flawed people. The problem is that they're flawed people with superpowers, which makes them a danger to the rest of us, even while they're trying to protect society. The Avengers are striving for a Nietzschean ideal, but every so often their efforts just wind up turning New York into a pile of rubble while they eat shawarma like a bunch of assholes.
Nietzsche would actually have been critical of most comic superheroes as an expression of the ubermensch, because they limit themselves with a moral code. Superman and Batman have a policy against killing because they think it's just morally wrong, but Nietzsche believed that any policy that relied on higher morality was a weakness for any self-respecting ubermensch because he believed higher morality did not exist -- a true superman would only live by his own rules.
Or, to put it another way, they would be all Hulk and no Banner.
This is where Ultron comes in, because Ultron really is the ubermensch, and in case you didn't know, he's the villain. When Tony Stark becomes disillusioned about the Avengers' ability to truly protect mankind, he creates Ultron, who immediately decides that the only way to achieve world peace is to kill, just, everyone. As soon as he appears, Ultron quotes the famous philosopher Pinocchio: "There are no strings on me." It's a succinct way of declaring that he's bound by no laws of man or God, just the way Nietzsche would have wanted it.
"My only limits are my own imagination and a slapdick script."