Fortunately or unfortunately, nuking asteroids for resources is an outdated scifi fantasy. Modern modeling shows that even small, 10-20km-sized asteroids would retain the material pulverized by a nuke. Gravity stands in the way and would be even more pronounced on larger asteroids like Psyche, which measures around 175km at its widest. Nukes can fracture asteroid minerals, but they really can’t cleave off chunks or boulders and send them flying.
https://cosmosmagazine.com/space/think-we-can-nuke-away-an-incoming-asteroid-think-again/https://www.vox.com/science-and-health/2019/3/7/18251559/asteroid-blow-up-how-toCompletely pulverizing/destroying the smaller asteroids requires something like 10,000 Tsar Bombas. And that power has to be directed and delivered in a short timeframe to overcome gravity. We couldn’t just drop a Tsar Bomba every couple minutes. It would be an insane weapon.
And even if we could pry chunks of ore off asteroids, we wouldn’t send them to low-Earth orbit to be processed, for a few reasons:
1) Miscalculate with a big enough chunk, and we’d put a crater in the Earth and whatever disastrous effects accompany the impact. No government or insurance company will cover that risk.
2) Miscalculate with a small enough chunk, and we’d burn it up in the Earth’s atmosphere and lose the investment.
3) It takes a lot of energy to slow down an object so that it enters Earth orbit, nevertheless lower the orbit to LEO. Energy = money.
For all these reasons, should asteroid ever become a thing, it will probably resemble terrestrial mining. Machines and/or people will dig/drill/mine material locally at the asteroid and maybe even refine the ore locally as well before shipping the product elsewhere.
And honestly, given how fast many asteroids are tumbling and the insane energies that would be involved in despinning them, the Venn diagram overlap of asteroids with very valuable concentrations of minerals at/near their surface and asteroids with accessible rotations may be vanishingly small. I was tangentially involved in NASA work about a decade ago to bring a very small (we’re talking truck-sized) asteroid to lunar orbit to give Orion/SLS something to target, and there were practically no candidates even though we didn’t care about whether the asteroids had economical ores.
FWIW, apologies for raining on anyone’s parade.