I would think precious metals get a lot less precious if they start falling out of the sky and I am pretty skeptical about other Earthside uses being profitable at all.
People that go try to live in space are going to have a hard time of it so I wouldn't expect profit from supplying space industry either (the longer missions cosmonauts and astronauts have completed have had grave physical consequences, we aren't adapted to low g environments).
Current space industry is dominated by intensively manufactured goods (satellites) that provide enormous value to ground based users. Having literal tons of steel available isn't going to help with the intensively manufactured part.
I can see space hotels or whatever, but that is not a huge market, even with Musky launch prices.
The other day I found an interesting analysis on that, which should answer all your questions: https://medium.com/@centrena/the-cislunar-economy-series-fed....
It enthuses that colonization should be the end goal because it will drive funding. I remain unconvinced that there are actually enough incredibly wealthy people that want to go die in space to drive a vast economy.
There's enough interest, demand and money in current space activities to justify a small cislunar economy; after that happens, well, hard to predict, but I think you're underestimating the amount of people with ideas about what to do in the Solar System.
Getting started, it could be a scheme of space development futures. Bet on the value of things in space, which puts money into the development of more things in space.
By 'in space' of course we mean everywhere in the Universe except tiny 'ol Earth.
Asteroid mining isn't happening in a vacuum (well, it is in a physical one, but not metaphorical). Fortunately, there are people working on using the mined material to manufacture things in space too; missions plans are being sketched around those capabilities.
It'd still be more cost-efficient to e.g. mine for gold under the ocean or in the Antarctic rather than send gear up to space to do that.
If we had a huge solid gold asteroid (how would that occur?) floating in a very close, very convenient orbit then maybe it would be cost-effective to send a ship to connect, re-orbit and land it without vaporizing; but anything realistic simply wouldn't be worth the launch effort&cost.
Seriously, not kidding. Lets push 3D printing so hard all we need to do is send a few drones worth "up there", and oila .. free everything for everyone, forever.
(This is actually a constant thing in spaceflight, that comes up because of the scales involved. Similarly to that, any engine able to cut down interplanetary travel to reasonable lengths (days, weeks) will have energy output of a WMD, and could be used as such.)