When we attempt to recreate those complex, planetary atmospheric phenomena in a box, we're doing so in order to measure and study them.
Making random turbulence in a box until it resembles the outside world, and calling it weather and extrapolating some predictive meaning from the result, is the total antithesis of what you're describing about why we come up with simplified models for impossibly complex systems. The purpose of [mathematical] models that are built thoughtfully is to explain why complex systems are the way they are, with data and algorithms, however imperfectly. [Whereas] The purpose of LLM models is to give the illusion of answering questions while never answering why the answer was given. The difference is the difference between a scientist and a tarot card reader, an equation and an oracle.
People have a well known tendency to gravitate toward the shamanistic, oracular, and superstitous. Listen, I ran a casino for 6 years, I know. The impossibility of knowing how 80 layers of matrix multiplication led to a particular answer is in itself a psychological factor in choosing whether to accept the answer or to question it. People tend to err on the side of the over, in sports betting terms... or on the lazy side in general... and they will make whatever excuses they need to after the fact to justify their decisions. So now we have a machine that can act like an oracle and which you can also blame, but the blame goes into a void because this machine is stateless and is only a reflection of information, not an intentional refinery of data.
Sit next to a bank of slot machines for an hour and listen to the absolutely ridiculous shit most people will come up with to explain how they "know" if a machine is going to pay out soon, and then tell me if you think it's a good idea to give them an LLM in their pocket to answer their questions in whatever way they frame them.
> The purpose of [mathematical] models that are built thoughtfully is to explain why complex systems are the way they are, with data and algorithms, however imperfectly.
Nope. The main purpose of the whole endeavor is usually to predict the behavior of a complex system, because that's actually what we care about. If we can predict it, we can adapt to it, and eventually use it to our advantage.
Explaining why a complex system is the way it is, is merely nice-to-have. Models are opinions. All of them are wrong, but some are useful, and we rank them by how useful they are. The models and explanations are important because, beyond their elegance and convenience, it's also the case that more accurate models give you better predictions across larger domains, meaning we get better at getting something useful out of the complex system.
People get fixated on modern theoretical science, with bottom-up mathematical explanations traced through seas of empirical data, with whole magical rituals of peer review and double-blind studies and statistical significance around them. But they forget that the core of empirical science is literally throwing shit at a wall to see what sticks. That is the guiding principle, everything else is just making the process more efficient.
Understanding complex natural systems (or even engineered ones that got too complex) always starts with tests - tests on the real thing, then on approximate models that we poke and prod and bash into shape until they start acting similarly to the real thing. It's through the poking and bashing, and how they affect our proxy model, that we glean insights into nature of the simulated phenomena, and eventually formulate general theories - but more importantly, the models give us useful predictions from the start, before we have any theories explaining why.