I understand that speed limits are too low, but you're comlaining about getting a ticket for doing something illegal, because the exact extent to which you were violating the law was off by a fraction?
The thing is with speeding tickets magnitude matters. There is a graduated scale for the fines with larger fines and more points for exceeding the speed limit by more. So yes it makes sense to challenge the magnitude. If you get a ticket for 12 mph over the limit the fine is say $150 plus 2 points (numbers I'm pulling out of my ass but are fairly representative), now if the automated camera is adding 4 mph more on top that puts you at 16 mph over which would then put you at a $225 fine and 3 points. This is a nontrivial difference.
On a side note, as a designer of roads and bridges I can say that the speed limits are influenced by the geometry of the road and the location (i.e. while it may be geometrically possible it is a bad idea to have a residential street posted for 50 mph). There are some cases where unscrupulous towns/villages/cities will post a lower speed limit than the surrounding areas as a way to increase revenue. This is can be challenged court and is frequently overturned. Also in areas where there are lower posted speed limits for things like curves (black on yellow) and construction areas (black on orange) the lower limits per MUTCD are not enforceable as those signs particularly the black on yellow are just suggestions. To lower the posted limit the signs must be the standard regulatory black letters on white they can only jump 10 mph at a time (i.e. you can't go from a 45 to a 25 in one jump) and there must be advance warning signs "reduced speed ahead". When in doubt about a speed limit or regulatory sign or even a traffic light timing consult a good highway engineering text and the MUTCD.