Computers are still Von-Neumann machines, and other architectures lost out due to the great returns on investment for that architecture. However, in the AI world, this might not be the case. For instance, neuromorphic computing is one example, and there are others. Or back to analog again! Superposition is instant—no slow adders with carry bits to propagate! Who knows. Fun times!
Most computers use modified Harvard architecture, funnily enough. There's a shared memory space like von Neumann, but separated caches for instructions and data.
It's the best of both worlds, because from the CPU's perspective it gets to have separate lanes for instructions and data, but from the programmer's perspective it's one memory.
Not always. Modern computers are like several computers networked into one, if you think about it. Since the DMA, that approach is not valid. Today we have IOMMU's.
The 9front/plan9 guys are trying to write a kernel (Nix) which wants to exploit every concurrent core of your CPU at crazy scaling levels.