The thing is, while the universe is full of metals, it's not that full of the materials needed to sustain life (as we know it, at least). You can find metals and other inorganic compounds on virtually every asteroid, moon, and planet, and many comets even. But water and nitrogen and carbon are significantly rarer.

Plus, life can't survive more than a few minutes in space without metal encasings and electronic life support; whereas metal alone only requires life at a much longer time scale. So, while it may be possible to build a fully inorganic self-replicating fleet, it's certainly impossible to build a fully-organic one with any technology or chemistry we know about today at least.

Carbon does not beat metal structurally. Some organic polymers are competitive in tensile strength. In flexural strength and fracture toughness, alloys continue to rule. And when carbon materials are competitive in strength and toughness, they tend to be highly temperature-sensitive and have sudden failure modes, which is not great for operating in space. Consider e.g. the Titan submarine that failed due to carbon fiber composite fatigue.

Life as we know it relies on a complex and interdependent ecosystem, and complex life relies on countless other organisms to support us. Without plants we absolutely couldn’t survive, without microorganisms we can’t survive. Without ample supplies of food, water and oxygen we can’t function.

Generally speaking the pace of biological activity is a lot slower than industrial ones too. We might make up for the pace with scale, but then you’re back to the hard problem of dependencies and “fuel”.

I’m not sure that the problem of beneficiation changes because the system is biological rather than industrial. Edit: Without carrying whole ecosystems with the probe at least.