Regarding market depression, it will take years if not decades to
get the volumes moving to have that impact. I did a bit of checking
http://www.nss.org/settlement/asteroids/RoleOfNearEarthAsteroidsInLongTermPlatinumSupply.pdfand it seems that terrestrial platinum sources are <1ppm platinum
(but it's so rare and valuable that's worth mining), whereas meteorite
(and thence presumably asteroids) are as much as 68ppm. That's still
a wee tiny amount, and a major amount of processing required, and sorting
out the other heavy metals (which are currently quite valuable, but less
useful, so far more vulnerable to price deflation), most of which will have
to be done here, I would think. I would guess they would be looking at
just a primary in situ processing - a quick cooking to concentrate the
good stuff and boil off the silica - solar powered, and definitely worth
it to get the return shipping weight down.
Anyway, where I'm going with this is that platinum is incredibly useful.
It is almost as inert as gold, has a very high melting point, which two combine
to making it desirable, in fact in some cases necessary, for use as containers
when cooking up high melting point substances. It also has all those well known
catalytic properties. As the price comes down, demand will go up markedly,
which will slow price deflation very quickly.
As to all the rest of those weird lanthanides, I don't know much about them
beyond that they're rare and heavy, but perhaps interest in them will result
in unexpected new uses. (They are rare because they are heavy, which means they
sank to the centre of the earth when it was molten, and we wouldn't have even
as much as we have now if it weren't for the Period of Heavy Bombardment, which
brought in a small amount on asteroids, which retain the primordial elemental
distribution, thus the expectation there'll be lots to find out there.)