i appreciate your question, since it clearly comes from a real newcomer to anarchist thought.
there are many many books that address the assumptions in your question, but simply put...
a) how people respond when they are held accountable for their own actions would be/has been different from when there is an outside agency that is supposed to monitor everyone;
b) who monitors the monitors? (ie, you apparently think the system works now, but there is evidence everywhere that it doesn't);
c) the idea that space exploration is beneficial (to anything except imaginations that have been stunted in other ways), or that medicine helps more people than it and its effects harm is effectively refuted in many anarchist circles;
d) anarchy wouldn't exactly be a situation of "do what you want". but whatever limits on behavior existed would be more accessible and human-scale than the global, international, national (lack of) influence we can have now as individuals or small groups of people;
e) the idea that people will murder and rape unless laws stop them is sad, and hasn't been my experience at all. there will always be people who murder and rape, of course, but they do now. i'm betting that the system that creates alienation from the world and each other, a sense of powerlessness and rage, is at fault for many actions that i want to stop. changing the system, and encouraging people to defend themselves and their own families and friends seems more appropriate and effective then paying a group of people to maintain order mostly for the benefit of the rich, and the status quo.
if you're actually interested in this question, let us know. i'm sure that people here will have lots of suggestions for good things to read.