I just wanted to ask about that: if they spun them for gravity, wouldn't they fly apart? Because you'd have a meaningful amount of gravity pulling the rocky surface away from the asteroid.
But even cladding the surface to keep it together, you're talking about many tons and tons of rock you suddenly need to keep together. At that point, why not make a space habitat completely separate from the asteroid? It seems silly to put your base on the gravity of an asteroid and then try to undo the gravity of that asteroid.
As long as a chunk of rock is in one piece (rather than a pile of rubble) it's not going to get pulled apart by a modest amount of gravity. Look at any cliff overhang (or the underside of any boulder) for proof. So the trick is just to pick an asteroid that is not a rubble pile.
Look at cliff erosion. Look at moons and asteroids being pulled apart just by differences in gravity between its different sides. I strongly doubt any asteroid of meaningful size is going to be strong enough to withstand meaningful rotational gravity.
But even cladding the surface to keep it together, you're talking about many tons and tons of rock you suddenly need to keep together. At that point, why not make a space habitat completely separate from the asteroid? It seems silly to put your base on the gravity of an asteroid and then try to undo the gravity of that asteroid.