An official accident report could accomplish all the same things. The officer could write in the report, “both parties stated that person x failed to yield at a stop sign and the on site evidence supports the statements.” There would probably be other evidence the office could likewise report factually without a citation. I don’t see why whether a citation was issued should change that in any way.

I guess the strongest two arguments to me seem like 1) adding a fine partially compensates the government for the use of an officer’s time and resources, and 2) it perhaps creates a more formal way to track dangerous drivers, like someone getting repeat speeding tickets. Absent drunk driving or something else much more significant than someone making a mistake, neither example seems compelling to me.

Reading the comments, it sounds like the policy decision varies by area.