Yes, capabilities are correlated but an open question is how correlated, and how much negative transfer (where the model regresses on other benchmarks) will come into play.

Why are frontier models not chess geniuses (amateur club level elos), despite knowing the rules deeply, having a great deal of chess data in the training set, and having general reasoning training in other domains? Similarly, a beginner can beat a frontier model at Magic The Gathering. Why?

It is because chess and MTG are not priority targets in the (expensive) training pipeline. Chess is already solved by lesser neural networks so there is no wow factor, and nobody cares if they suck at MTG.

Mathematics on the other hand, has a huge wow factor, and a large and highly verifiable dataset.

Related: why did OpenAI give up on video?

I agree it's disorienting and scary but I'd phrase it like this: "the moment we come up with a systematic, objective way to verify a task, *and we can generate or find large datasets, and somebody has a reason to pay for the expensive training*, we become obsolete at it."

The economics side of it is an important constraint, currently ignored because the big labs are swimming in money (debt).