I'm not an expert in these metals
All I can say is that palladium likely has a lot wider use in industry (for example, car making) than the other precious metals. This metal is known for its extremely high absorption capacity of hydrogen. This property allows to use the metal as a medium for efficient and safe hydrogen storage. Indeed, it may be not as efficient as liquid hydrogen itself, but I don't think many people would want to drive a car which can easily turn into a sort of "hydrogen" bomb, especially after someone actually gets blown up
Using Palladium for the storage of Hydrogen can be terribly expensive. Because it may require many ounces of Palladium, just to store enough Hydrogen to power the vehicle for 200 or 300 km. And considering the remaining Palladium reserves around the world, I have to say that they may be enough for only a few thousand vehicles at the most.