> Once in orbit, it takes very little energy to go to an asteroid and to launch that asteroid to a parking orbit compared to dredging mountains of soil and rock on Earth. The yields would be extremely high; there's more gold and platinum in some Inner Belt asteroids than we've ever mined on Earth so far, and it's just floating there for you to grab and bite chunks out of.
This is not true at all. This is laughably absurd. Getting from Earth's surface to LEO takes about 9.8km/s of delta-v but then getting from LEO to another destination requires more delta-v. To get to the Moon requires another 6km/s of delta-v on top of the 9.8km/s you needed to get from the ground into orbit. There's a reason the Saturn V was a giant rocket with a teeny tiny capsule mounted on top. Getting places in space requires a lot of propellant.
Here's a nice list of NEAs and the delta-v required to reach them (one way) from LEO[0]. The list is very helpfully sorted by delta-v requirements. You'll notice that the easiest NEA (2018 AV2) requires an additional 3.758km/s of delta-v. The easiest to reach NEA on the least requires more than half the delta-v that it would take to land on the Moon. Once you rendezvous with an asteroid you need to come home which requires yet more delta-v (thus more propellant). Moving an asteroid to orbit Earth is not in any way as simple as you might think from reading science fiction.
So there's nothing "very little" about the energy required to land on an asteroid let alone land on one, mine anything useful, and then return it to Earth. There's also the complexity of the vehicle needed to do the mining. Platinum (pure platinum mind you) goes for up to $37k per kg.
Even if we pretended that all of the technology existed and was donated and we just paid for a Falcon Heavy launch (about $150m to get about 17t of payload to an asteroid) we would need to ship back 4t of pure platinum to Earth just to break even. Even if you assumed that in the best case platinum was a thousand times more abundant in an asteroid than Earth's crust[1] that's still only 5ppm! You'd need your asteroid miner to process about eight million tons of ore (if my math is right) to get that 4t.
If our asteroid miner is 17t or so how long do you think it will take to process that much ore? The loan for the Falcon Heavy would have defaulted long before it would be even close to finished. There's just nothing asteroids have that ends up being worth the cost to mine them instead of mining them on Earth. Don't forget besides raw ore Earth also has lots of landfills literally filled with stuff than can be recycled and valuable materials extracted.
Materials in space are only really useful to an entirely space-based industry and the only way to bootstrap a space-based industry is to launch it from Earth which is basically just lighting money on fire.
[0] https://echo.jpl.nasa.gov/~lance/delta_v/delta_v.rendezvous....
[1] https://en.wikipedia.org/wiki/Abundance_of_elements_in_Earth...