These issues can all be worked around of course but personally I'm far more in favour of an insurance black box.
Most poor driving I see is well within the speed limit; aggressive acceleration, braking, cornering - a black box can take all of that into account because usually you find that if someone is an aggressive driver all of the numbers are right up even if they're not speeding.
(I'll add a bit of bias here - I have designed hardware and written software for black boxes in the past)
I don't disagree with you, however, tech isn't always perfect.......
When our Daughter first started driving we had a black box for insurance - no problem, and it was quite interesting (especially for our Daughter) to look at the start and try and get the best safety score. One day I was driving, and the stats showed a lower score for cornering which occurred when we were going round and round the multi-story car park