Energy is everything. As already noted, with free energy we would be able to create elements instead of mining it.
For space mining we would need to reach orbit with an heavy payload, go to the the asteroid, land, use a lot of energy to probe and mine materials, escape the gravity of the asteroid and come back to earth. I cannot extrapolate any good number but the cost of orbit seems to exponentially grow for biggest ships, and this is a huge ship. Maybe you can do it cheaper with nuclear explosions project-orion-style, but meh.
I suppose that at the current energy costs this is not convenient even if you do not consider the billions in hardware and research.
You don't mine the asteroid in-situ, you fly it back to earth (or lunar) orbit and mine it close to home (scifi type stories are typically based on options that are not available to us in reality). You basically only fly a (or multiple) engines out there. FWIW, asteroid gravity is pretty nominal (why they are asteroids and not a planet) but that's not really relevant to the scenario I'm describing anyway.
Here's an article that seems relevant. I don't have time to give it a deep read right now though.
https://space.nss.org/technologies-for-asteroid-capture-into-earth-orbit/Get it into orbit and use it to tether a space elevator.