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So you're disagreeing with the thread proposal? Because this is big direction from someone like youAbout cosmology questions, some information about tiering.
First of all, String Theory isn't natively about small-scale extra dimensions. Brane Cosmology is also a part of String Theory, both the small and large extra dimensions are branches of String Theory that try to explain why the extra dimension isn't seen, one states that they are super small and so from our perspective they have all been eliminated due to dimensional compactification, the other states that they are big and exists outside of the brane that limits our world in a higher-dimensional bulk. Both are answers to strings needing extra dimensions, so it's not a case of "if there are strings, they need to be compact".
However, the fact that they were talking directly about finite curled dimensions makes that already clear, even if no string theory is mentioned.
However, that doesn't eliminate all the possibilities for large higher dimensions. If what the others are talking about is the sea of quanta having more types of physical worlds than just that one is true, it could be possible for those different physical spaces to have large higher dimensions. After all, a multiverse can include universes with a different set of laws of physics.
Another point is that although large dimensions are a way to have valid qualitative superiority, that is also not the only way. If anything the main reason why compactified dimensions don't scale naturally to larger tiers is that they are often not portrayed as giving qualitative superiority and in our system we assume that large dimensions are already giving qualitative superiority. If qualitative superiority is still proven in the series, even with compactified dimensions, I think it should be enough for higher tiers.