It seems that it must be a really difficult problem to work out the optimal solution for having spare capacity to allow time/location shifting of workloads to minimize carbon per unit of compute. This Dell paper[0] suggests that 16% of the carbon over a typical server lifecycle is from the manufacture, so you probably don't want a server sitting there unused for 23 hours per day, since the overall carbon/compute rati…
Carbon consumed in building a server is sunk cost and would be paid independent of whether the server does any kind of carbon-footprint-aware load shifting. Assuming the server is "sitting unused for 23 hours a day" is the wrong model for what this work changed. You're assuming the server could be running at 50% duty cycle vs. 100% duty cyle. It isn't; since we're talking the batch load, there's a roughly fixed amoun…
If Y = 2 and only 16% of the carbon in a typical coal-powered computer's lifetime is from the manufacture, then solar makes sense - solar is 2*16% = 32% of the carbon of coal. But if Y = 10 - so it's running 10% of the time, meaning there need to be 10x as many computers built - and 16% of the carbon is from the manufacture, then solar power is actually worse for the environment than coal power: solar takes 60% more carbon than coal power.
Of course, this is a vastly simplified situation, but it points to the idea that we need to at least consider the carbon cost of manufacturing.