To be fair, if you take your agument from the last paragraph, i.e. that the function of chess as the game is to entertain, your earlier argument re: min-max doesn't really stand, does it? I think, you're right that chess probably quite interesting in terms of abstract maths, like surely there are ways to represent the pawns (pawn structures?) as well as the pieces (knights, bishops, etc.) in terms of some supersymmetry. However, it doesn't seem like much progress has been made in this area academically since the 20th century. It may be helpful to tap into AlphaFold and related results for interpretability! Stockfish has incorporated some probabilistic programming (neural network-based) but it's comparatively small-scaled, and behind SOTA of the bleeding-edge Transformer architectures (in terms of interpretability, nonetheless!) Surely, if we can't get supersymmetries in some complex forms, we could get ahead with the modern interpretability and RL techniques. Given the appropriate knowledge representation, by combining self-play with known playing sequences and behaviours by forcing the model into known lines, & perhaps partitioning by player styles so there's incentives for the model to learn some style feature, it should be possible for it to learn what we refer to as the essence of the game, i.e. archetypal human playing styles comfortably. Using insights learned from interpretability, it should be possible to further influence the model during inference.

If they were to get to that point, we could say that chess would be solved...