Another goal we have is low latency (and high clock rate, which is depenend on low latency), which suggests putting everything in a qube or even a shere. So we compromise somewhere in the middle with a square with a few layers.
Made me think of this:
https://en.wikipedia.org/wiki/Menger_sponge
Say we have roughly 300 sq mm, that's about 17.32 mm square, which is 8.24e+7 silicon atoms (0.21 nm) across.
Then we have a surface area of roughly 1.36e+16 atoms - the area x 2.
If we make a fractal sponge down to the limit of single atoms, then that's about 16.5 cycles of removing cubes from a 17.32 mm cube. Let's ignore the difficulty of doing it half a time. According to the formulas from wikipedia, the result has a volume of about 0.7% of the original, with 2.4e28 "sides" of atoms exposed.
So the third dimension gets you about 1.8 million times the surface area. I suppose this isn't nearly as good as 4e10 flat sheets with 1 atom separation between each, but you could argue it's more practical because everything is connected...