Ask 100 people what their definition of AGI is and you'll probably get 100 different answers.
My definition is closer to DeepMind's "can do any [computer-based] task that a human can do", and certainly a human intern can learn on the job and do better on day #2 than day #1.
Learning is basically THE hallmark of intelligence. Being able to learn from experience and use that to do better in the future.
If you could somehow take everything the LLM learnt today and "put it into" an update for tomorrow that would be better than nothing, but the intern on the job is probably learning dozens of things per day that stack upon each other, so that's going to be a S-L-O-W learning AI intern !
Leaving aside the technical issue how you could store a days learning, or what that would even mean, you've also got the privacy and merge issues if this were to be done in the cloud without every customer having their own personalized model.
For real continual learning we need to get past gradient descent-based batch training and develop a new learning algorithm so the model itself learns incrementally as it runs (animal-like predict, observe, learn cycle), rather than being reliant on some external alien to come in, equipped with it's entire learning curriculum, and program its weights.
OK, let's say we get continuous learning today, what does tomorrow look like?
I won't argue that AI can do some learning as context sizes are still terribly small and expensive to iterate.
What does the world like in a week? A month? A year?
How long before these models drift to their own languages? To their own set of morals? To their own alignment?
None of these questions are answered and I'd rather stay at AGI-lite until they are as having a billion agents going off in their own directions seems like a recipe for disaster.
With current models and their general knowledge self learning just seems like you'd have a few ASIs crop up really quick.