>>11189414>the anchoring devices could also try to steer the asteroids closer to earth to make them viable.Sure, but if you've got the time and resources to steer an asteroid that close to earth, you've probably got the launch capability to get into space cheap already.
There are other types of skyhooks and fountains that could launch you into space without needing to coral an asteroid, or use your asteroid as the counterweight to a space elevator.
Railguns aren't a bad idea (if you could make them more efficient) but you've still got the problem that your load would need to survive some crazy G's at launch.
If you were on the moon, or mars, with its lower gravity and air pressure your rail gun would be more effective than earth for the same energy debt. If you were on mars you could build your launch ramp up the side of olympus mons.
There's also a minimum speed your asteroid would need to be moving to keep itself from crashing into earth.
Not to say it would be physically impossible, you've just got a lot of practicalities that would need to be hammered out.