>>The issue is, speeding fines are in place so that cops can stop you and make the motorway safer.

Not really. They exist as a revenue source for the police department. This is why people routinely drive 10-15 mph over the speed limit and yet don't get pulled over - except when the police need additional revenue.

>>In any case, I don't think there would be a way to monitor your speed to any kind of accuracy from a moving object.

It doesn't have to be 100% accurate. There's a certain margin after which the small inaccuracy that results from measuring speed of moving object A from moving object B becomes inconsequential. If the police vehicle is driving at 65mph (the limit) and you're 10mph faster, that means you're over the speed limit.

The whole idea of measuring the speed of moving object in any given moment is not an optimal solution. It is much better (and easier) in many cases to measure the time in which it took a car to travel some distance. You just set up ALPR cameras every few kilometers and record travel time. If the limit is 60km/h and you managed to drive 20km in 15 minutes, you were clearly over the limit at some point, and therefore you should be fined.

I think France uses this system. Also there was a huge uproar on the news of potential introduction of it in Poland. Mostly because it's so effective.

EDIT:

http://en.wikipedia.org/wiki/SPECS_%28speed_camera%29