I can give you an answer because I had been one of those who either wrote or verified the specs of semiconductor ICs.
Legally and ethically speaking, I could only sign off on the parameters within which we have verified the IC/processor would work. And then my boss, and her/his boss, and everyone else would see the evidence of the tests, and they too would sign off on those constraints.
I could not ethically or legally sign off that a batch of processors would work at -100 C, if I had not put them thro the suite of tests at -100 C.
If you chose to use your equipment at -50 C, equipped with the processor I signed off on with a low threshold of -15 C, my company would no longer have any obligation to that processor. You have broken the warranty.
Testing at -50 C is a lot more expensive to do than testing at -15 C. I would have to verify the test site is actually -50 C--. It is also very dangerous.
Besides that, special/hermetic packaging is required for ICs to operate at extreme low temperatures. As an extreme example, plastic packaging could develop cracks or structural compromises when we pour liquid nitrogen onto them.
Differential expansion between the die and the packaging could tear the die away from its site of attachment, or crack the die.
There are stress tests that include simulating temperature variations in the functioning of the IC. Say your laptop is sitting in your car in frozen temperatures of -10 C. You turn it on and within 5 minutes it reaches a temperature of 85 C. And for the whole winter, you did that every evening. What about the head unit and the computer-controller that sits in your car, which you would drive for the next 15 years subjected to such fluctuations every winter in northern Maine?
There were too many mechanical issues that my mechanical engineering colleagues had to deal with when it comes to extreme low temperature testing. So, how low a temperature would you want us to verify and how much more extra are you as the consumer willing to pay for that low temperature testing?
We cannot just test one or two units to verify the absence of mechanical issues like incompatibilities between die and packaging, unlike people who hot rod their motherboards experimenting overclocking with the mere one or two processors they bought from ebay. We have to design the acceptable statistical distribution and the sampling plan that would fall into that distribution, that would apply to a stream of ICs flowing thro the product line.
Occasionally, the legality of the constraints could be rather involved, where the US govt agency requires the OEM to have their representative present while we test those ICs/processors, which could take a few days for a batch. That representative would sign off that we indeed had performed such tests at such constraints. That is how a $100 processor would cost the US govt $2000.
Such that if the US govt agency somehow decided to operate the equipment beyond the tested and verified constraints, we would no longer be legally held responsible for any mishaps or future malfunction.