Whether the judge will lower the fine or drop it completely depends on his mood and how much the county needs income. But you will not pay any more than the original amount, so try it anyway.
If you don't pay and they wrote your driver's license number correct, you will be screwed in 3 places.
1. The ticket will be mailed to the rental car company since that's where the car is registered. The rental car company will be force to pay the fine. Then they will send the bill to you. If you don't pay, they will blacklist you so you can't rent from them again, and they will get a collection agency to go after you. This will mess up your credit history, so you won't get credit cards or loans in the future.
2. The DMV computers are connected in all states. This will go on your record in your own state.
3. If you are not a greencard or US citizen, INS will deny you entry at the border if you have outstanding traffic violation should you try to leave and come back to US.
So I suggest write the letter, then pay the fine if they still want you to.