Some of the tests may need to be weighted differently
Which is why the data should be made publicly available, so the weighting can be checked. I'm fine with them saying that Score X on head-on colission at 60mph is worth less than Score X on rear-end colission at 15mph simply because the first probably leaves you in a world of hurt anyway and isn't nearly as likely to happen as some jackass rear-ending you at the lights.
may not even be able to be weighted in a rational manner
...just means gut-feeling work. That's not a test.
It's an approximation, an educated guess at how safe a vehicle is
The whole point of testing isn't to make guesses. You can't just go around running a bunch of tests, getting measurable data from it, knowing with some certainty what the error in the test methodology is, and then check the alignment of the planets before factoring the test score into what a bunch of tea leaves say.
you can't really claim that one car is safer than another based on the score
...would preclude a stars rating entirely. If there's no demonstrable greater safety in a car with 5 stars vs one with 4 stars, then why does the first have 5 and the latter 4 to begin with? And if there is that demonstrable safety difference, then surely the one with 5 stars can at least claim theirs is safer than the one with 4 stars. And if that is the case, assume there was never a car with 5 stars before - they surely could claim that they do have the safest car evar.
I do get the psychological, PR and industry flak aspect that the NHTSA is trying to address - but that would be a lot easier by dropping the scores and only issuing stars.. or by keeping the scores and dropping the stars.