This is how it breaks down. Unless you're doing ninety in a school crossing or DUI, the city managers have to work on volume, not quality. They set up "traffic schools" so the judges can more efficiently skim the big ticket losers and not waste their time on nickel and dime stuff. The clerks have been quietly instructed to just take your money if you offer any as well.
When you insist on going to the court at the appointed time, the cop never shows up. He's earning more money out on the street workin' the folks who will just pay without wasting their time. Unless you are obviously expecting to see the perp, the judge will just have you pay up anyway.