>>10
Given the strength of the earth's gravitational pull, I'd say such a thing would require tremendous amounts of power (almost certainly not worth it), and a power failure would mean total collapse. In addition, strong tensile material is still required because only the part near where the projectiles recoil experience an upwards force. The intermediate material feels a pull in both directions, and is likely to be torn apart. A possible counter is to chunk the structure into multiple units, each sending pellets to the unit above.
>>11
Exploiting existing resources: small investments, low risk, high gain
Exploiting new resources: enormous investments, enormous risk, enormous gain
Given that most executives aren't ready to randomly blow a few billions dollars on such projects, it should not be surprising that these projects are still mostly non existent.
The other thing that needs to be determined is the constitution of these asteroids. Wikipedia suggests that most of these contain large amounts of carbon or silicon compounds, which are useless, given their abundance on earth. Even the metal ones are only useful if they're a solid block of metal. If they're some oxide compound of metals, then they're just like most other earth rocks, and would take a tremendous amount of energy to purify (which is why metal refineries don't attempt to refine any random rock they see).