There has been some progress towards 3D design. But thermal issues are going to be important. CPUs run hot even without reducing the surface area for cooling, eg 1.4 billion transistors in 130mm^2 on mine, generating 77W at design speed. Or a fair bit more when I overclock mine.
So very low power designs are needed for deeply 3D processors.
As to the original question, I believe that the problem is soluble if the computer has enough storage space and time.
Whether there will ever be enough of that to achieve that even in a million years of design and building before the machine can be even turned on is very debateable.