What you're describing is often referred to as "molecular nanotechnology" (MNT) or "atomically precise manufacturing" (APM). Yes, technology is headed in that direction and I hope that with the arrival of strong artificial intelligence, these kinds of molecular factories can be developed quickly. While I think that a mature APM won't resemble biology very closely, I do think that the molecular-scale mechanics of biology can be used to bootstrap our way toward those more mature machines.

I strongly recommend looking into the writings of Drexler and Feynmann on this topic. While I've been reading about this potential tech since the 1980s, my first real introduction to the concept was via the book, "Nano!" by Ed Regis. The key for me was realizing the parallels between biology and nanotechnology. One can think of a cow as a "machine" for transforming grass and water into beef. While the concept of nanotech is not exactly akin to biology, it should be capable of similar products. While a theoretical APM box should be capable of making beef, it should just as easily be capable of making anything else we can model at the atomic or molecular scale - computers, televisions, clothing, solar panels, housing and construction materials, food, robots, etc. - quite literally anything we can imagine. But instead of "growing" these products over a period of months, the directed machinery of a mature APM could crank these products out in a matter of minutes or hours.

It's a really exciting topic and I'm sorry to see it's not as widely discussed as it should be. It is the ultimate in technology and it's one that will completely transform the world - likely the entire solar system and beyond.