Rare earths are neither particularly rare, nor particularly likely to be unusually abundant on a Planet 9.
However!
A Mars or Earth-sized planet sufficiently far out in the solar system might be sufficiently cool to be able to retain helium in its atmosphere, without being a gas giant planet. If so, it might conceivably be the best place in the solar system to obtain 3He, an isotope that has considerable attractiveness for use in fusion reactors. A D-3He fusion rocket might even provide a nice way of getting out there and back in a reasonable time.
I don't see how the "attractiveness" of helium-3 is anything non-zero. If you can't even fuse deuterium with tritium, which is the easiest thing there is, helium-3 fusion goes out of the window.
DT is certainly easier to fuse, but it presents very difficult, IMO likely intractable engineering problems. D3He would finesse those problems (neutrons, material damage, tritium breeding), and potentially enable direct conversion of fusion energy to electrical energy (or, perhaps, more volumetrically efficient transfer of thermal energy to coolant). So IF the physics can be made to work, D3He could end up being more practical.
The company to watch on this is Helion, and perhaps Princeton Satellite Systems.
The moon has 3He, at a concentration of maybe 10ppb, in regolith the heating of which would use more energy than the released 3He would yield in fusion.
Helium at cosmic isotope ratios is 120ppm 3He. So if there were a planet out there with an atmosphere of this helium, extracting the 3He would be much easier (just compress, liquefy and separate, which you'd have to do with lunar helium anyway.)
The technology and infrastructure needed to reach Planet 9, build a mining outpost, then transport everything back at a profitable cost is likely decades if not centuries away. That’s not counting the fact that Planet 9 is so far away that getting there with current technology is a lengthy affair in itself (the New Horizons probe wouldn’t even be halfway to a theoretical Planet 9, and it’s been flying for over 15 years!)
Not saying I don’t want this to happen - I would love nothing more than to have humanity push out into the solar system, but recycling or scavenging is infinitely more of an realistic option.
The fastest man-made object ever launched was the New Horizons spacecraft. Headed on an intercept course for Pluto 30 AUs away, it took 9.5 years to get there. And that's without slowing down; if you actually wanted to land on Pluto you would need to spend even more time actually slowing down. The object in the OP is 225 AU away (which is dramatically closer than prior estimates of the distance of Planet 9 (300 AU)). All this means that, even moving as fast as we have ever launched a spacecraft, it would take at least 70 years for a probe to reach Planet 9, even without taking time to slow down. A probe launched today would return with its cargo no sooner than 2160. That's probably never going to be economical, even with future improvements to spacecraft propulsion (moving faster just means you need more and more fuel to slow down, at which point you are beholden to the tyranny of the rocket fuel equation).
It's easy to forget the scales here. We're used to Pluto being our reference point for "far edge of the solar system", and it's easy to conclude that Planet 9 is about as far as Pluto, but it's so much farther. Voyager 1 is a bit more than halfway that far.
I dont mean to take away anything from your post - but wanted to mention that the parker solar probe has now beat new horizons for fastest man made object (if you don’t count the manhole cover :) )
Indeed, but the Parker Solar Probe is cheating, since it's going so fast because it's literally plummeting into the sun--the exact opposite direction of a deep space probe. :)
We have plenty of rare earths here on our homeworld. If we run out (which we won't), we'll scavenge before we build the trillions of dollars of infrastructure necessary to mine the solar system.
Or we could, you know, build mining and manufacturing facilities on a planet that's, say a couple of AU away, instead of a couple of hundred AU. There's reasons we've done neither.
Rare Earth metals aren't actually that rare. We even have a lot of big mines that are closed right now because its not profitable enough yet and many other sites enrirely undeveloped.
However!
A Mars or Earth-sized planet sufficiently far out in the solar system might be sufficiently cool to be able to retain helium in its atmosphere, without being a gas giant planet. If so, it might conceivably be the best place in the solar system to obtain 3He, an isotope that has considerable attractiveness for use in fusion reactors. A D-3He fusion rocket might even provide a nice way of getting out there and back in a reasonable time.