I don't even know where to begin with telling you everything that is wrong with all that you just said.
Instead of initially refuting them one-by-one, which only creates an argument on your terms, let me set the tone of an argument on my terms.
You present a strawman's argument instead of valid points worthy of serious debate in regards to the original statement. You make a weak, passing reference to anonymity being about more than trolling and then reference emotionally loaded examples to support said references.
Now, to refute your points individually.
1) Muggings often happen in public and private settings. You can be on a busy street, or in an ally, a public place, or even your own home. Two of my friends (who are here on HN too) were mugged in Rome a couple of months ago. Those fellows got away with their stuff and never caught, I believe. I've also had friends who were mugged in other situations, were able to give descriptions of their attackers, and those criminals have been arrested later because the public and police are on the lookout for them. The lack of anonymity doesn't prevent you from being a victim of crime. Many crimes such as mugging are committed by repeat offenders who are well-known to law enforcement. Being anonymous or not does not prevent crime from happening.
2) You reference the supposed possible threat implied by children being attacked at some future point by an anonymous deviant. This is a common tactic most often used to prop up weak arguments by appealing to the possible fear in parents. Statistics and reality quickly discount this notion. First, most acts of sexual abuse against children are committed by relatives. Not random strangers. Secondly, due to the extreme lengths over the last 20-30 years that this fear tactic has been used in the U.S., today we have massive online publicly available databases of people even remotely associated with sexual acts against children. The possibility of someone with such a history moving into a neighborhood near a school is more remote than at any time in history.
There was even a story the other day on MSNBC where a happily married couple met in high school. He was a few years older than his then girlfriend, she was 15 and he was 17-18. Her father didn't like him and reported him to the police after it was revealed they had started having sex. Despite that they have been married for years and have 4 children together, to this day this man is still labeled as a sex offender.
The restriction of anonymity and freedom for the majority should not be severely restricted simply because of an unfounded fear tactic, which is what you imply.
3) Third, you reference the 9/11 attacks. This is the most emotionally charged topic to happen in the last 10 years. One that the U.S. has spent tens of thousands of lives and TRILLIONS of dollars to "combat". There was nothing that was anonymous about the men that boarded those planes.
http://en.wikipedia.org/wiki/Hijackers_in_the_September_11_a...
To quote, "Within minutes of the attacks, the Federal Bureau of Investigation opened the largest FBI investigation in United States history, operation PENTTBOM. The suspects were identified within 72 hours because few made any attempt to disguise their names on flight and credit card records. They were also among the few non-U.S. citizens and nearly the only passengers with Arabic names on their flights, enabling the FBI to identify them and in many cases such details as dates of birth, known or possible residences, visa status, and specific identification of the suspected pilots."
The failure to prevent 9/11 lies more in the faults of the U.S. security apparatus then any ingenuity on the behalf of the hijackers. Read up under the Pre Attacks section I reference in the link above.
Finally, to refute your last point and to sum up my argument, there are more costs to being known rather than being anonymous. Being known makes it difficult or impossible for the innocent to seek freedom, to examine their rights, or in many cases to even conduct financial transactions. To set up a panopticon surveillance apparatus to closely monitor a population for their "security" reduces the cultural and financial health of that society.
People that are extremely publicly known get away with horrific crimes often, right in front of everyone. This ranges from murder to sexual assault to massive financial crimes.
Its more expensive morally and socially to be watched than it is to be anonymous.