I think sleep serves multiple functions. For example, anyone who works out in any-what systematic way knows that sleep is essential for muscle grow. You can't skip on sleep if you want to get fitter. And this probably has very little to do with the more sophisticated functionality of the brain, rather it allows for some process in muscle tissue to happen.

So, whether the LLM "dies" in any sense may or may not be important for what "sleep" is defined to be in this article. It's quite possible that sleep also affects endocrine system in animals or hormones etc... and that's what's causing death, not necessarily anything to do with how brain functions.