The Eckmann-Hilton argument is one of the cleanest results in algebra. Given two binary operations on the same set, with a shared unit, that are compatible in a precise sense, the operations must be equal and commutative. You do not choose commutativity. It follows. The compatibility condition is the premise; commutativity is the output.
Benjamin, Markakis, Offord, Sarti, and Vicary (arXiv:2501.16465) generalize this to weak globular higher categories. In these structures, cells have boundaries — source and target — and the boundaries themselves have boundaries, recursively, through all dimensions. When a cell's boundary is sufficiently degenerate — when enough of the recursive boundary data is trivial — all composition operations on that cell are equivalent and commutative. The result applies in every dimension simultaneously.
The mechanism is the same as the classical argument scaled upward. Two operations that see the same boundary data cannot produce different outcomes because the boundary provides no information to distinguish them. In dimension one, this is the original Eckmann-Hilton. In higher dimensions, the degeneracy condition is stricter — more of the boundary must be trivial — but the conclusion is the same: composition collapses into a single commutative operation.
The structural point is that commutativity is not a symmetry you impose. It is a consequence of informational poverty. When the boundary of a cell is too degenerate to distinguish different compositions, the compositions must agree. The symmetry is forced by the absence of structure that could break it. This inverts the usual framing where commutativity is an additional axiom — an extra requirement placed on top of an algebraic structure. In sufficiently degenerate higher-categorical contexts, it is the default. Non-commutativity requires boundary richness; commutativity is what you get when the boundary has nothing to say.