Based on my experience in Ohio, The prosecutor will lower the fine or drop the points, if you show up.
When I went to court, I signed in. The prosecutor was the person signing people in, accepting your plea. The rude prosecutor told me:
<ticket was ~75 in 65)
Her: how fast were you going?
Me: Like 67, if that.
Her: Well that's speeding, so you are guilty. GO ahead and pay the fine and save us the time.
Me: What's the point in me even coming down here then?!?!
Her: That was your decision.
Me: Well, I would rather try my luck with the judge.
Her: Ughh... we have a full docket today! FINE! You are scheduled for [3 hours later]
...
30min. later of me sitting and waiting.
...
Her: Ok, we agree to drop the points and lower the fine from $120 to $0 if you pay $50 court costs.
Me: Deal!
Point of the story... if you go before the judge, you will get reduced punishment, or you can strike a deal with the prosecutor to save them time. The courts have more important cases than traffic violations.