I think I would make some modifications to your proposal to make it more realistic.

First, I don't know if you intended this, but "stimulating the universe" carries a connotation of a low-level physics simulation. This is computationally impossible. Let's have it model the universe instead, using the same kind of high-level pattern recognition that people use to predict the future.

Second, if the AGI is simulating itself, the predictions are wildly undetermined; it can predict that it will do X, and then fulfill its own prophecy by actually doing X, for any X. Let's have it model a counterfactual world with no AGIs in it.

Third, you need some kind of interface. Maybe you type in "I'm interested in future scenarios in which somebody cures Alzheimer's and writes a scientific article describing what they did. What is the text of that article?" and then it runs through a bunch of possible futures and prints out its best-guess article in the first 50 futures it finds in which the prompted premise comes true. (Maybe also print out a retrospective article from 20 years later about the long-term repercussions of the invention.) For a different type of interface, see microscope AI.

If this is no longer related to your question, I apologize! But if you're still with me, we can ask two questions about this proposal:

First, do we know how to do this kind of thing safely? I think that's an open problem. See, for example, my self-supervised learning and manipulative predictions for one thing that might (or might not!) go wrong in seemingly-harmless versions of this type of system. Since writing that, I've been feeling even more pessimistic because, to make the system really work well, I think we might have to put in various kinds of self-awareness and curiosity and other motivations that make for much more obvious types of risks.

Second, if we do make such a system, does it do the things we want AGI to do? Well, I think it's a bit complicated. If we use the system directly, it always needs a human in the loop, whereas there a lot of things that people might want AGIs to do directly, like drive cars or do other boring and/or safety-critical jobs. On the other hand, we could bootstrap by having the prediction system help us design a safe and aligned agential AGI. I also wrote about this last year at In defense of Oracle ("Tool") AI research and see also the comments.

Is your suggestion to run this system as a source of value, simulating lives for their own sake rather than to improve the quality of life of sentient beings in our universe? Our history (and present) aren't exactly utopian, and I don't see any real reason to believe that slight variations on it would lead to anything happier.

I think we can expect to achieve a lot more than that from a properly aligned AGI. There is so much suffering that could be alleviated right now with proper coordination, as a lower bound on how much better it could be than just effectively running copies of our timeline but at lower resolution.