But... at every cell division, two half cells will be built. So after twenty divisions, there will (on average) be a millionth part of the original cell in ever

But... at every cell division, two half cells will be built. So after twenty divisions, there will (on average) be a millionth part of the original cell in every descendant. I don't really see the point in creating all organelles outside a cell. When we copy the functionality chemically, the results are very different. (Air planes not flapping their wings, etc.)