Asteroidal water as a prerequisite to precious metals
Something to keep in mind is the effect your delta V budget has on your propellent to dry mass fraction. Larger Delta V budgets mean less dry mass that can be devoted to structure, thermal protection, parachutes, and/or wings.
I picked 4.4 km/s exhaust velocity because that's near the best you're going to get with chemical propellent.
It takes about 9 to 10 km/s to get to Low Earth Orbit (LEO). Remember, some of the dry mass fraction must also be payload. So just for getting to LEO, your dry mass is around 4 or 5%. This puts constraints on how robust you can make the structure or how much thermal protection you can add.
On re-entry, the space shuttle would shed around 8 km/s over an hour's time. This would subject it to high temperatures and large dynamic pressure.
For ascent shuttle's Max Q was around 35 kilo pascals. A strong hurricane has a dynamic pressure of around 3 kilo pascals.
These constraints have made it impractical to re-use rockets. The space shuttle did this in limited fashion (although it would throw away dry mass enroute). But maintaining the thermal protection tiles was so labor intensive little if any money was saved.
So water is one of the first commodities Planetary Resources hopes to mine. Given an extra-terrestrial propellent source, it would no longer be necessary to climb in and out of earth's steep gravity well to get the propellent needed for a spacecraft's continued use.
And economic, reusable spacecraft are a prerequisite for mining platinum, gold or any other precious metal. If a space craft is thrown away each trip, I believe even an asteroid made out of pure crack cocaine would be a money pit.
Oxygen is more storable in LEO
Hydrogen and oxygen propellent depots are a problem in low earth orbit. Not only do you have the sun for a heat source, but the earth is a ~300 Kelvin heat source that takes up nearly half the sky. The Multi Layer Insulation (MLI) heat shades would need to be cones that cover most the depot's sky, leaving only a small area to radiate heat into. Also some aerobraking drag passes would probably be used to park the propellent tanker in LEO. For parking in LEO, drag passes can save up to 3.1 km/s but they are time consuming and heat the rocket, two factors that exacerbate cryogenic boil off.
Both oxygen and hydrogen are cryogens, but hydrogen needs to be kept much colder and is harder to make an effective seal against. Oxygen typically accounts for the lion's share of propellent mass is a lot easier to store. So if we get water from asteroids, I'd expect the propellent sent to LEO would be mostly oxygen.
But ULA's Kutter and Zegler have proposed propellent depots that use hydrogen boil off for station keeping: Realistic Near-Term Propellent Depots. Hydrogen boiling off acts like evaporative cooling. So the inevitable hydrogen boil off not only serves for station keeping -- but also keeps remaining cryogenic oxygen cold.
Getting the platinum to earth's surface
So I'm assuming asteroidal propellent in LEO. How much is needed for a soft landing? That is an open question. I'll note that SpaceX looks like they're well on their way to recovering their boosters. But these don't re-enter the atmosphere at 8 km/s as an orbital cargo would.
But we can look at energy savings. Kinetic energy goes with square of velocity. Assuming the usual aereo braking re-entry sheds 8 km/s of velocity we can look at energy differences for different scenarios.
Shed 2 km/s with propellent leaves 75% percent of the velocity to shed. .75^2 = .56. So 56% of the energy.
Shed 4 km/s with propellent leaves 50% percent of the velocity to shed. .50^2 = .25. So 25% of the energy.
Shed 6 km/s with propellent leaves 25% percent of the velocity to shed. .25^2 = .0625. So 6% of the energy.
Besides propellent for reducing energy, it is possible asteroidal stuff could beef up structure and thermal protection thus making the space craft more able to endure re-entry.