"If you admit you know that you were breaking the law, you will be ticketed. That's why they ask you. "
Not always the case. I've admitted to going over, and was let go with a warning. If you're busted, you might just as well 'fess up; there are other ways to fight the ticket.
Only if the cop doesn't show up in court? How could a person plead not guilty if he already admitted to the officer that he had been speeding?
Officers are just collecting evidence. As long as you are polite you will be ok. There is no reason to admit guilt. What purpose does "fessing up" serve?