This idea is so the majority of people around the world can be safe. This would be able to keep track of super villains meaning less superheroes would be needed. When superheroes get into big fights they cause damage to government property and most likely kill and harm people. If a superhero battle took place in your city and your mother died because a collapsing building wouldn't you want to know who was responsible. This rule would keep more villains in jail. Super humans are the ones who choose to be superheroes, by doing this it is a risk they take, but it's simply not needed.
If you say yes, you could easily argue that you could keep peace, protect your country, etc. The thing is though, you would keep peace by fear. That one country with the better or bigger amount of super humans will literally be dominating the world. Everyone would obey the laws, afraid of getting zapped or painfully killed by the super humans. In other words, my argument is that this would tip the balance between countries all across the world, which would also make the word "mortal" a whole new bottom class or have a whole new meaning.
That is the question of the upcoming film Captain America: Civil War. The registration act would force all superhumans to reveal their identities to the government and act as a police force for the authorities. I'm on Captain America's side; anonymity is essential for these people. This was also briefly addressed in the first X-Men film where Jean Grey and Senator Kelly are debating mutant registration; Jean Grey opposed it, arguing that to force mutants to expose themselves would further the hostility and fear they are already facing from the wider community, whereas Senator Kelly was staunchly in favor of registering and regulating mutants, his argument being, "We must know who they are, and above all we must know what they can do". Scrutinizing any one particular group of people more than others is prejudicial: what if Muslims in America were registered or if the government decided that people with Asperger's Syndrome need to be monitored after the Sandy Hook shooting?