>This is seemingly in opposition to your statement. I think the diff comes from considering all the other energetics - precipitation of CaO from the hydroxide is thermodynamically quite favorable, reducing the overall theoretical cost by 65% relative to the chloralkali process. So to the extent that Heimdal can usefully harness that energy gradient, that's the difference.

I guess the crux of my argument is that it is impossible[0] to capture the energy from CaO precipitation. E.g.[1] one has to spend 2J of electrical to create the hydroxide in Ca(OH)2, but the 1.5J get released on precipitation of CaO comes as heat[2], rather than a reduction in energy input.

So, in summary, Electrochemical CaCO3 would have [approximately] equal theoretical electrical demand to chloralkali and, to borrow your term, a higher reality factor overhead[3], to make a product an order of magnitude cheaper than NaOH.

[0]For a loose definition of impossible, to be fair reality's never quite so black and white.

[1]Made up numbers.

[2]And heat in sub-boiling water is not useful for doing work.

[3]I broadly agree with your position on reality factor overhead, just made less of an emphasis on it trying for 'equivalent but worse and creates less value'