OK, mathematical fact: if your average speed between two cameras which are not consecutive exceeded the limit, then there *must* be at least one pair of consecutive cameras between which your speed exceeded the limit.
The proof of this is left as an exercise for the reader, as some of my textbooks used to say.
Suppose there are 4 cameras 1, 2, 3, 4. If your average speed over the whole stretch 1-4 was too high, then it must have been too high on 1-2 and/or 2-3 and/or 3-4. Without loss of generality, let's suppose it was 1-2. Now if you were prosecuted for speeding on the 1-2 stretch and also on the 1-4 stretch, that would be two prosecutions for the same offence. I think we all think that's not what would happen. So you can be prosecuted for 1-4 or 1-2, but not both. (And in fact you can also be prosecuted for 1-3; another exercise which is left to the reader.)
What would happen in practice? It seems overwhelmingly likely to me that you would be prosecuted for 1-2. There's just no point designing the system to calculate the speeds over the stretches 1-3, 2-4 and 3-4, because it's mathematically guaranteed that if you exceeded the limit on one of them you'll also have exceeded the limit on 1-2, 2-3 or 3-4. And imagine how many combinations the system would need to look at if there were, say, 15 cameras in one long stretch! (Answer: 105, and for N cameras the number of combinations is N*(N-1)/2, the proof of which....)
So the simplest, most straightforward system is just to calculate the average speeds between pairs of adjacent cameras. It cuts down hugely on calculation and data storage requirements and it doesn't miss any opportunities for prosecutions.