First of all - such asteroid need to exist in the first place. Much more likely that there are asteroids which have higher concentrations of rare ores compared

First of all - such asteroid need to exist in the first place. Much more likely that there are asteroids which have higher concentrations of rare ores compared to earth, but nowhere near being "mostly of out them". Second - humans need to locate this deposit. Remotely. In the asteroid field. We are still finding out deposits in the habitable Earth regions, because that is a hard task, talking about locating deposits in the Belt is an impossible task, and will remain so for a long time. Third - we need to get there. Excluding flyby's, the best humanity managed is to deliver two 1 ton vehicles to the Mars. And there we had a luxury of aerobraking to save a lot of fuel. Belt is way farther, there is no aerobrake possibility and we will have to deal with other asteroids along the way. We don't have such tech. Fourth - we will need to strap engines to the asteroid, remotely, with an hour signal lag. Engines which don't exist in any form today. And we need to get fuel to them somehow. Impossible task. Fifth, we need a Moon colony with robots or humans. Sixth - high energy tech on the Moon. Seven - launch facility on the Moon. And I've probably missed a few other impossible hurdles, writing this. Then IF all of that would exist, you would need it to be at least as cheap as Earth based mining, which is a pipe dream. Any space tech is more expensive by design, sometimes orders of magnitude more expensive. AND finally there need to be an infinitely elastic market on Earth for this new source of materials. Imagine you will sell a billion tons of platinum tomorrow, the price would crash and never ever recover. You see this yourself in your last sentence.