While the total amount of platinum-group metals in asteroids is many times greater than what is accessible at the Earth surface, because on Earth these metals have gone down, into the Earth's core, they are much more difficult to extract on asteroids than on Earth.
At the surface of Earth, the platinum-group metals are concentrated into metallic nuggets or metallic sulfide crystals, which are very different in density and chemical properties from the surrounding minerals, so they can be separated relatively simply.
On asteroids, these metals are present mostly as minute impurities in iron-nickel-cobalt alloys (i.e. around one part per million). Separating them mechanically is impossible and chemical separation requires great amounts of chemical reactants, e.g. of a strong acid, that would also be very difficult to produce on asteroids, which are depleted in volatile elements. Perhaps one could do some kind of distillation of liquid metals or a differential sublimation in vacuum, which would require a huge amount of energy and a lot of special equipment able to work at very high temperatures. Bringing back the PGE-containing iron alloy is impossible, as its weight is about one million times greater.
At this time there exists no technology that could be used for the extraction of platinum-group metals on asteroids. Developing such a technology is possible, but it is something much more difficult than making a spaceship going to an asteroid and back.
Any credible company that claims that they want to mine asteroids would have to first demonstrate on Earth how to extract the valuable chemical elements from the minerals that can be found on asteroids, and only then solve the simple task of transportation to the asteroids.
There are some celestial bodies where the platinum-group metals are found in forms that are easier to separate from the surrounding minerals, i.e. in the sources of the so-called chondrite meteorites, which are very small bodies that have never coalesced into big asteroids. There the minerals remain as they have condensed at the formation of the Solar System, without having ever been remelted. There much of the platinum-group metals may be in the form of microscopic refractory inclusions in the big mass of common minerals, e.g. inside the so-called calcium-aluminum rich inclusions, instead of being dissolved in iron.
While a survey mission could find such small bodies with a chondrite-like composition, the amount of valuable metals in each such body is very small (a few grams per ton) and the energy consumed with moving from a small body to another would be very large in comparison with the amount of extracted metals.
Moreover, no operations would be possible on such small bodies, the spaceship would have to contain inside the complete metal extraction facility.
What should be easy to make on asteroids is only high-quality iron or nickel or cobalt alloys, for building structures in space, not on Earth.