Well, generally, I’m assuming we want some of this energy on Earth, and some of it to be used to boost other rockets, and to generally move things around the solar system with. Now, I’ll even say that I’ll believe you that beaming microwave energy to earth is impossible. (I say nothing about solving parts of the problem by lifting the reception station high in the atmosphere. This is a technical problem, technical problems have solutions.) But generally, if the mining facility is to be on the moon, we’d want most of the energy to go there, too. If you want individually target satellites, fine, that works too. But generally, these satellites will be out of the plane of the elliptic (you don’t want them blocking energy to planets, so you’re going to need to bounce them off something to send the energy to the destination, so I figure, since there’s going to be, at least at start, a single redirection point, there might as well be a single reception point.
I’m aware of the issues of lunar dust. Perhaps a lagrange point will be better. I’m not fixed on a static refinery. I’m just giving the simplest possible solution I can think of to the issues. One of the points I have is that we’re going to want this stuff in the vicinity of earth, one of the points is that we’re going to want all of these various metals together, and one of them is that we’ll need a load of energy to deal with it. Further, we’re going to have to deal with control lag the further we go out, and the less gravity there is, the worse it’ll be for the poor bugger who will have to be on site, and there will need to be at least three.
My main point about keeping things on or near the moon is that having the works there, will keep it useful to us here on earth, as well as making it easier to build in the first place. Your movable refinery is a superior product, but I’m talking about a first-gen solution.