Let me count the ways.

1) thrown out, cop did not appear
2) I've had fines reduced from hundred's to $50 or less. (last example I have was using cell phone in Chicago, reduced to $20 from I forget how many exact hundreds they wanted if I had just paid the ticket)
3) Pay the fine but am granted supervision (so essentially dropped if I have a clean driving record for 3-6 months)
4) Pay the fine but violation dropped to a non-moving one.
(I can't provide cost saved by insurance premium not going up for the last two points)

Also, let's not forget if one has a company car, having a severe speeding ticket or other traffic violation come to the attention of one's employer is not worth it no matter the financial cost to fight it.

so yes for me and my many experiences, it has ALWAYS been to my benefit to go to court or to have someone appear for me.