What mineral is there possibly on an asteroid that such a plan would actually produce a profit?? The bigger the asteroid, the higher the energy costs of nudging it into Earth orbit. How much did it cost to bring back a few moon rocks? Name anything that costs even 5% of that amount.
China doesn't need to make a profit. It just needs to get shit done and they take the long view, not live by the next quarter market results. That's a huge advantage.
Besides, this isn't a real scientific problem, not even an energy delivery one. Don't put nuke reactor motors on the thing, hang a huge solar sail to gradually alter the orbit. That's doable. Returning and asteroid for earth mining doesn't seem efficient, but if you wanted a source of raw material for exploration vehicles you have it right in orbit. Of course new techniques for refining and manufacturing items in space is right there.
When someone wakes up and realizes that Earth launched space vehicles are as dumb as a mud fence and builds a space elevator there will be a way to put hardware into orbit to complete the needed supply chain.
We can have ships moving throughout the solar system in a hundred years. It seems they will most likely have Chinese names.