"Being able to settle is something only the guilty SHOULD find relieving."
That said, if you're in court, you're pretty much guilty. It doesn't matter that you've done nothing wrong (no "innocent" plea, remember?); you're in their court, and that means someone has charged you and is demanding payment. "Guilty" means "to pay", according to Black's/Bouvier's. that means that Not Guilty is somewhere you don't want to be (committing a commercial dishonor in their court == contempt).
Just pay the fine (you can pay with securities/commercial paper if you don't want to use cash/cheques), and be done with the matter. Once you've settled, file a motion to expunge with a higher court in order to clear your record.
As the guilty, I guess I find being able to settle pretty relieving. :)