The thing about companies mining in space is actually interesting.

I don't disagree.

As of right now, a lot of our technologies are held back based on not having enough access to rare-earth metals such as gold, lithium, platinum, etc.

I see what you believe, I however don't think "a lot" of "our" technologies are held back due to a lack of rare earth metals. If that were so I believe we would have more market pressure to recycle said metals. Elon Musk... I get the feeling that what he wants to do and what will be done might differ, and I don't think the difference will be decided so much by the availability of lithium. I would guess that the success or failure of his endeavors will have more to do with corporate and governmental actions (or non-actions).

This however invokes a further question in me. If we were to be forced to evacuate the earth and live somewhere else, would we still continue with earth-based industry?

Uh, hrm.... Yes? But, in a different way. I mean it depends way too much on what you consider the traditions of earth-based industry. I doubt humans will treat the rest of the universe with too much more care than they (we) have Earth. My guess would be that we will have some form of space based slavery. That hangs on my definition of slavery.....

Odd to have this thread pop back up.