In Cook County, at least, you're given a time to appear in court. Everyone appears at that time. Cases are handled in alphabetical order. But: if you have a lawyer, your case is handled first --- the lawyers are on the clock, you see --- so there's about an hour and a half of waiting for lawyer after lawyer to come up and get their clients cases dismissed, while everyone else sits doing nothing.
No but in all seriousness it's a good time if you like talking/learning/debating cryptography and general security things.
People without lawyers didn't know that all that's really important is that you pay fines to the court. You're taking the court's time and you have to pay for it.
They tried to deny they sped, the cop said they did, and the ticket stuck.