I'm aware of three-dimensional storage hardware, but only at archival speeds. https://en.m.wikipedia.org/wiki/5D_optical_data_storage

(It's so-called five dimensional because you have polarization angle and color in addition to physical position)

In hard drives, reading off a single track is the fastest op, and reading off of sequential tracks is the next fastest op. I’d count that as a feature of the 2d geometry of the disk