Geometry only benefits from visual reasoning in 3d and lower, and there are a lot of dimensions above that!

You can see visual reasoning as a little cheat computation, you can run math problems through your sense-determining brain, which is what brains are really good at (robots struggle with our levels of dexterity). But the fact remains that you can only visualize in low dimensions, and there are infinitely many dimensions.

Note: You can reduce many problems to 3d, but also many problems in 3d have configuration spaces with much higher dimension, so there's some nuance.