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/a smaller set of weights for the same LLM./

Distillation is alive and well... Earlier work on model printing also found that it's pretty easy to find smaller sets of parameters which can replicate the behavior of the entire network with pretty good fidelity.

Large parameter counts give space to explore, and give routes out of what would be local minima in a lower dimensional space.

In other words, there's no guarantee that any given trained model is a minimal representation of its training set.

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I'm not claiming any arbitrary set of weights is a minimal representation. But typically, if people could achieve the same quality of results with a smaller set of weights, or weights which have been quantized to lower bit representations, etc, they would have published the smaller one instead.
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You kind of are claiming they're minimal, though. Because if they're not, your statement that "if you found any patterns in there, you could exploit the regularity..." implies nothing. Yeah, the patterns are there, and people are exploiting them.

Your socioeconomic argument just doesn't hold either. People don't delay releasing models until they've minimized it to the theoretical limit. They ship it when it's good enough for whatever job they're making it for.

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The weights aren’t compressed. So there are interpretable redundancies in practice.
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If the weights arn't compressed, then a smaller set of weights would perform as well. Sure, you can always induce as much symmetry and patterns as you want by bloating the data set, but that hardly gives us insight into how a set of weights which is "as full as it can be" of information.
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The point of TFA is that there are regularities you can exploit in the actually existing weights of machine learning systems, not in some hypothetically maximally efficient weights. The maximally efficient weights would indeed have no structure, but that’s not what anyone is working with.
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