They aren't boxes. They record wild accelerating, braking and cornering. Drivers who aren't terribly good wildly accelerate, corner and brake. Wheel-spinning little chavs pay more for their insurance, sensible driver pay less.
They encourage smooth driving through lateral and longitudinal acceleration limits. You could be ticking all the smooth driving boxes according to their system but driving an inch off the bumper of the car in front. I wonder if you could do a brake stand/rolling burnout at a gentle walking pace and not exceed the accel limit - green light, good driving! To get round this they would basically have to log all data like an F1 car and have your driving peer reviewed by a panel of stewards.
They are so very nearly a good idea, but it doesn't take much imagination to come up with a whole bunch of real world scenarios where a good driver is punished. Perhaps fit them as a punishment to vehicles owned by those done for certain driving offenses?
I would much rather share the road with people properly trained to drive appropriately to conditions and have at least some idea of what the car is capable of, with the mindset to use that performance appropriately and where the risk to others is minimal. Unfortunately I don't have an answer to that, but I'm pretty sure the answer is not making everyone afraid to do anything but doddle gently along because some software says that >0.25g (or whatever the limit is) counts as bad driving. Removing responsibility from the driver to decide what is safe is the wrong approach, I can just imagine now "but my insurance app said I was driving safely, therefore the accident wasn't my fault"
Additionally, how can you say they aren't boxes, they ARE boxes! Some are phone apps, true, but others are actual boxes that someone has to fit to your car. An "engineer" has to crawl around behind my dashboard or wherever, chopping wires about to fit one of these? No thanks! I wonder how clever the apps are, if you chuck your phone in the door pocket and your phone rattles around, or if it drops on the floor will the app think you've done a barrel roll?