First there are no DA or prosecutors in PA for traffic offenses.
It is you, the police officer and the magistrate. The only time a plea is offered is on the date of the hearing. The only person who will offer a plead or no point ticket is the police officer and the fact he gave a road side discount I highly doubt he would take another step down.
Next, it seems to be standard operating procedures today that a ticket is issued at most all accidents. I have no fact on this but it appears that this is done to ensure your insurance goes up even if you choose not to file a claim with your insurance company which many people are doing these days for minor accidents.
Case and point, a friend hit a deer a few months back and as required he call the police to notify them of a dead deer in the road. An officer showed up and ask what happen and simple put the deer jumped out in front of the car. Well the officer issued him a ticket for driving too fast of conditions, and he justified it by saying there was deer crossing sign a mile back and since he was warn of this possibility he should have slowed to the point that he could have stopped safely.
Here is an accident which was no fault of his own, and the insurance company recognizes it as such but now that he has points on his record his insurance will most likely go up anyway even though this guy choose not to file a claim since it was rental and he paid the deductible himself.
You could try fighting the ticket, but the fact you hit someone on the other side of the road says you left your lane of travel, hard to dispute that fact. These are tickets are just an insure to your injury.
I am not a lawyer nor am I in law enforcement,
I will not make any value judgment on why you're asking a questions.
I will try to provide information so you can make an informed decisions so take it for what is worth and do your own research.
Remember it is easy to tell someone they will lose verse providing knowledge.
Lastly, I have no vested interest in your outcome win, lose or draw and the same goes for anyone else.