Just to make it clear - It would not crash (I’ve just tested it), but will throw a warning.
I agree that there are some parts of the core which needs refactoring, and that it doesn’t makes much sense to try make them notice free as they are.
However as far as I checked, situations like that are not that common. Our codebase get much better over the last years, but unfortunately the new code often also introduces notices. This means that we also need to educate contributors and keep an eye on the topic during review.
We will never reach notice free code if we keep postponing it for later. So chunk by chunk we should improve it. Personally on my dev TYPO3 installation I’m keeping notices visible, so it’s easier to spot the most common ones.