Nobody needs to worry about storage density in the sense of how much shelf space you need for cold storage. Tape, NAND flash, and even high-capacity hard drives are all dense enough that the incremental cost of more shelf space is not the most important part of the problem.

And NAND flash is already pretty 3D, with hundreds of layers of memory cells fabricated on the surface of each wafer, and several such dies stacked in each BGA package, and it's not uncommon for U.2 drives to contain two PCBs each with NAND packages on each side.

Tape is a way to get volume. Through easily spooled layers. Not fast access but otherwise not unreasonable. Plus tapes stored outside of the drive.

Another way to look at it: "and yet here we are". Tape is still what has led to the highest density so far (depending how much storage you look at, and cost tradeoff). But also cost tradeoff of separating the drive from the medium. which hasn't really worked: LTO tapes are pro supplies - and so, expensive.

Good thinking - there are many projects around this. Ceramic, DNA, 3d glass, etc. They all run into the same IO problems tape has though.

Tape on a spool is 3D volumetric storage

Tape is generally available, I don't think in of those more esoteric storage medium, like 3D glass cubes are commercially available.