This is a false premise. It doesn't have to do anything this fancy.
You can expect that any given asteroid is likely to have a certain amount of iron, carbon, silicon, nickel, etc.
In almost any solar system, you can mine the materials needed for construction very easily. Solar gives you enough energy to do (slow, deliberate) resource extraction from asteroids.
As for propellant and reaction mass, we already know nuclear explosions work excellently. Unfortunately, based on analysis of meteors we don't expect asteroids to have great heavy-metal concentrations; on the order of 10ppb for Uranium. This presents a challenge, but not an insurmountable one; it just means that you'll probably want to get explosive materials closer to the center of the system.
> Not even viruses, the most aggressive and efficient self-replicators we know of, have managed to consume all the biomass on the planet, or could reasonably be expected to do so.
This is true, but 100% irrelevant to the challenges of creating space-based manufacturing capable of reproducing all its own components.