As a former police officer with the New Orleans PD in the late 60s, I can offer a point of view based on extended observations of traffic on main urban thoroughfares. From my observations, the single factor causing most auto accidents was following too closely. Next in order of accident causation was driving too fast for the prevailing conditions (heavy traffic, rain, ice, snow, etc.).
A speed limit per se, except in isolated circumstances, seems unsuited for its intended purpose (protecting against accident and injury). It would better serve the public if police officers were to concentrate on those driving faults that actually caused accidents. Speed limits, however, are easy to enforce. Other violations are more difficult to prove and consequently cause officers to spend more time in court.
A ticket book in those days contained 25 tickets. Patrol officers (those who handled calls) were expected to write at least 4 ticket books a month. Traffic officers (those who were assigned solely to traffic violations) were expected to write at least 4 books each day of duty.
At no time was the word "quota" mentioned during pre-shift roll call meetings. Nonetheless, each officer had better be regularly asking for more ticket books from the duty sergeant.
In the United States today, writing speeding tickets is generally accepted as a means of reducing traffic accidents. However, again from my perspective, it is not the ticketing of speeders that reduces accidents, but rather the increased attention level of drivers due to the acknowledged presence of police officers on the roads.