"Should Public employees think that they are some kind of elete because of a badge?"
Did they get it in a box of CrackerJacks?
What's elete? Oh, you mean elite.
The answer is they earned the right to wear it - the badge means something. They're getting paid to do a job that can be dangerous, think of that whatever you like. They didn't order their badge from an ad in the back of a comic book or a gun magazine.
John