I'm suspecting asteroids will eventually be utilized as a source of construction material for orbiting research and manufacturing activities. Governments on Earth will continue the long tradition of a central power wanting to impose its "benevolent" will on distant territories. Some groups of independent minded miners will take a few asteroids in tow to establish a slowly moving colony beyond the reach of government authorities in interstellar space. They will plot their course toward another system so their distant
descendents will have the option of settling that system (on a planet or in orbit) or slingshoting back into interstellar space.