Very cool theory but I always wondered how can a virus replicate in cells of people who are, well, dead? How would the natural selection you describe even work?
Your body is a collection of trillions of cells, all of which are in their own way individually alive, and work together for the greater good of the organism that is you. So when you die because of a critical failure, it's actually that the organisation of these cells to function as a whole has been fatally compromised: but the cells themselves individually keep going. Your brain cells last for a few minutes. Your muscle cells for a few hours. Your skin and bone cells for a few
days. And if they're still going, so can any virus using them. And maybe a virus could repurpose them to a new organisational capability.
The logic here might be that the virus carries genetic material capable of altering human cellular activity sufficiently to continue functioning under the conditions of organism death. Let's put cards on the table now: it's not realistic. That's too much genetic alteration, too much of our bodies are set up to work in specific conditions. (Bacteria, more plausible: they're much bigger to carry enough genetic material, but even still effectively creating a massive replacement genetic code is a phenomenal task.).
The obvious limit is oxygen and energy requirements. The energy requirements for undeath would have to be incredibly low (zombies are cold, implying vast metabolic reduction). They're slow, also implying low metabolism. Mostly anaerobic respiration, then? The lack of blood flow is immensely complicating, as it the primary nutrient transport system. So maybe the zombie cells have some other way of passing nutrients (e.g. gap junctions), or maybe there's some form of interstitial fluid pumping. Perhaps they can go into forms of extreme "hibernation" if not being used.
Anyway, I could go much further, but the point remains that it might be - at an extreme - theoretically possible to rewrite enough genetic activity of cells such that they are capable of some functionality even in undeath. They'd need to be modified beyond the point they could reasonably be described as human cells, though.
The other complication is how does this transition occur? Does the virus set everything up ready to go, and when the off-switch flicks on the human, it takes over (how would that work)? Does it need to move really, really fast once death occurs and start the re-write then, and what's stopping it re-writing before death?