Name 10.
Hell, I will make it easy for you, name 1.
Difficult and very important to society?
Police Officer
Fireman
Teacher
Social Worker
If we want to talk about really difficult and important, we can talk about the thousands of scientists, mathematicians, doctors, and computer scientists in NASA, NSA, DARPA, DoD, DoE, and nearly every other government agency.
Seriously? Of all the jobs that you listed there only one is considered an exclusive function of the government, and that is only because they made it illegal for anyone else to do it. In fact, California use people who are actually in prison to fight fires, so the argument that firefighters have to be government workers is so stupid it doesn't even merit as an argument, yet it is still better than the arguments that teachers and social workers are proof that we need government employees.
Come to think of it, anybody who has enough money\, and actually cares about their security, doesn't rely on the police, they pay private security people for protection, and have them investigate crimes.
Nice attempt though, not that you will see how stupid it actually is.
I'm not sure what point you're trying to make here. The fact that there is a private-sector need for these jobs is exactly why we need to offer teachers and police competitive salaries.