I like the general ideal of having cold, hard data to help investigate car accidents. But I'm skeptical of the ability of the government as a whole to use the capability in an intelligent way.
As with a lot of technology, the problem is that it can encourage tunnel vision that ignores things outside the scope of the technology but within the scope of the problem trying to be solved.
The perfect example is trying to use a black box to determine fault in an accident, which I can imagine will be among its first uses. Except that while a black box can't measure every potential factor in an accident, it can measure some of them, so the natural inclination will be to base accident fault entirely on the factors that a black box can measure. So going even the tiniest bit over the speed limit might make you automatically at fault (since the black box could measure speed), but driving while checking your email on your smart phone won't be considered, since a black box doesn't know you were doing that.
Of course a black box COULD be used intelligently, but that has not been how this kind of technology typically gets used. Think of the ridiculously aggressive use of speed cameras and red light cameras in many areas, despite the fact that they have a questionable contribution to road safety and divert resources from other things that might have more impact. I fear that black boxes in every car could easily turn out like those.