I was thinking this, and figured it wasn't viable for CPUs because they're already near the limits be being reasonably air cooled.

It's probably good news for RAM and SSDs, though.

They don't. You get twice the transistors, twice the power, and more than twice the cost (because the bonding itself costs money). See GPUs where power is increasing from 700 W to 1500 W. Moore's Law without Dennard scaling is kind of meh. You do save on networking because you need fewer servers.

Dark Silicon. Having proportionally less transistors firing at any given time.

More component count often let's you run same perf at lower clock (Nvidia 2000 series mobile chips had more cuda cores and lower clock than desktop and could match it at lower TDP).

You are right that geometry suggests a volume(heat generation) to surface area(heat dissipation) issue arising. You clearly don't want to build a sphere of pure compute layers.

But with the ability to stack compute layers AND non-compute layers of varying thickness you now can have most any 3D shape you like. There will be adverse effects that distance will have on spacing things out of course.

Maybe stack a bunch of compute rings to form a hollow tube with liquid cooling though the middle and outside?

Or reverse that and have multiple compute sticks hanging off a baseboard dipping into your cooling vat like some reactor homage.

I think liquid cooling will become more commonplace.

Early days yet and brighter minds than mine will make things work but I am optimistic for the future!