What is described in the OP is therefore not a specific characteristic of sleep. It may however be a "useful" rhetorical device.
I do however object to the extensive use of such rhetorical tricks in the conversations that surround LLMs. For example, why does a consumer-grade LLM display "thinking" while it is actually sending data from my computer to some datacentre, processing it, and sending the result back? Equally, why does it output human-emotive phrases such as "sorry" when such computation is revealed to be incorrect?
Such rhetorical tricks, and more, likely underlie to a large degree the popularity of LLMs, despite their actual performance being clearly below what the rhetoric implies.
You're talking about different things: biological necessity and evolutionary benefit.
You can find out about the former by preventing an animal from sleeping (but otherwise provide all other needed things), and seeing if it will eventually die.
That is actually almost impossible to do. The rat study was as close as we’ve ever come, and it’s still debated whether the rats died due to lack of sleep or some other mechanism, since the autopsy couldn’t confirm a cause of death. (It could have been due to the way the experiment ran, for example, not the lack of sleep.)
Meaning: it might just provide a big advantage.
I don't want to overextend and assume that any advantage extends to LLMs. That rest-and-recuperate advantage might also extend to LLM-based AIs. Or maybe not, and the rest-and-recuperate is mainly useful for biology-based organisms. But there is some logic to it.
> The function of sleep in animals is largely obscure.
In my understanding, it's well-understood that sleep is used to consolidate and store long-term memories (amongst other functions, like cell and muscle repair). They've found this memory-consolidation-during-sleep even in relatively simple animals like bees.