Why, even animals sleep? And if you for example learn an instrument you will notice that a lot of the learning of the muscel memory happens during sleep.
Yes, i could imagine something like a humanoid robot, where the "short term memory" is just a big enough context to keep all input of the day. Then during "sleep" there is training where the information is processed.
But I also think that current LLM tech does not lead to agi. You cant train something on pattern matchin and then it becomes magically intelligent (although i could be wrong).
Imo an AGI would need to be able to interact with the environment and learn to reflect on its interactions and its abilities within it. I suspect we have the hardware to build s.th. intelligent as a cat or a dog, but not the algorithms.
