I think all of your points are valid. I also think that we have optimized heavily for this state of technology. If we figured out that analog computing was somehow superior in a big way, I bet we would find ways of reducing power etc in analog designs.
One way that analog computing would be really neat for neural networks is in speed. The way it might not be so great is in reliability (or repeatability, specifically.) Analog systems are more susceptible to noise as well as variation from fabrication processes. Running things at saturation makes them easier to design, test and mass produce.