Where do you get this information that qweve got the technology and the overall ability to do what you propose? Wed have to haul out a processing facility to space (I dont think that we are short of silicon,, so we dont need to mine that anywhere but here).
What technology does it take that we do not possess? We can certainly do the math to get to the asteroids. We can build the rockets which will get there. We can build machines with which to mine ore from the asteroids. We can use that ore to build more permanent facilities and bigger machines. Et cetera.
Why pay to haul a processing facility into space, when we could build
one from the materials we find there? The problems involved are engineering problems, not theoretical ones. Humanity has an excellent track record solving engineering problems.
I do not pretend that it will be easy; but I cannot see which stumbling block makes it impossible to do the things that need to be done, with today's technology.
If certain metals (like Tantalum) are needed, wed have a radically different process chain than just "heating it to melting" wed have to convert it to a Flouride salt then process that.
My comment about INCOMING loads going awryy is a real concern. Whenwe go out into space with a shuttle and a load, the amount of fuel is calculated and known within safety tolerances. If we start making steel in space, we have to have an equivalent amount of a fueled up vehicle that could encapsulate and protect the metals from either burning up or causing destruction on entry into the atmosphere.
Foam the metal. Shape it like an arrowhead and spin it on re-entry to provide stability and distribute friction heat across it's surface. Splash it down in the ocean, it should float without much of a problem or be easily recoverable. Once again, there's no theoretical reason it won't work, so we should give it a try.
BUT; the larger point is that we don't want
to put the metals back on the surface! We want to use them to build stuff which will STAY in space. That's the true reason for doing all this, not to increase our bounty on the planet itself.
MAybe when we build the space "elevator" will stuff like this become more a reality (or we should ask ourselves, what are we running out of that we cant get by mining the earths mantle any deeper (Mantle mining has about the same problems but IMHO, they would be more easily solved.
Space elevators are extremely dangerous, I doubt you will see one around the Earth ever. Imagine the chaos if it came down.
The problem is not that we lack materials here on the earth, it's the fact that they are all at the bottom of a gravity well, and therefore extremely expensive. We need to find sources of metal and materials which are not locked up in gravity wells in order to fuel expansion into space.