Source: https://bulbapedia.bulbagarden.net/wiki/Special_Traits
While only the original Pokémon Rumble game that was available on WiiWare actually has randomly appearing Shiny Pokémon, later installments in the series would still introduce something as compensation for the removal of random Shiny Pokémon in the form of a new Special Trait. I've talked about this in other threads in greater detail, but the Epic Trait in Pokémon Rumble Blast and Pokémon Rumble World (both being 3DS titles that would later have a cartridge release) actually has the same odds of appearing on a befriended Pokémon in each of these games as a Pokémon in core series games has of being Shiny. Pokémon Rumble World made a significant change from the previous game with its Epic Pokémon, however- in this one, you can actually have as many of them as you want. Or I guess I should say, as many as you can find.
Epic hunting is such a criminally underrated side hobby that's provided me with
several hours of entertainment compared to Shiny hunting for a couple of reasons. The main draw is that unlike Shiny Pokémon, Epics actually play differently compared to their normal bretheren. Shiny Pokémon in the original Rumble game did have Special Traits too, but they weren't any different Special Traits from what any other Pokémon might have, meaning that Shiny Pokémon were still largely an aesthetic change in that game. Having missed out on quote "real Shinies" in a Rumble game, due to out on the original WiiWare game, playing through stages as one normally would for the sole purpose of hunting Epic Traits in Rumble World is a fantastic replacement, with added bonus of actually having all the Pokémon up to that point unlike the original WiiWare installment.
The similarities between Shinies and Epics don't end there, though. Whereas you can only Shiny hunt certain Pokémon using certain methods, you can also only find certain Pokémon in the Rumble series by playing specific stages over and over again. My favorite area to hunt in is Pokémon Rumble World's "Changing Land" stage, which is the closest any Rumble game has ever gotten to a randomizer mode- a feature that would usually make Shiny Hunting infinitely more exciting in my opinion.
I'll stop talking about this now so I don't distract the conversations here away from actual Shiny Pokémon experiences, but for my money's worth, Epic hunting provides a very similar experience with more fulfilling Pokémon gameplay as a reward for your patience. I might be alone in thinking this, but adding Epic Pokémon alone would instantly improve my enjoyment of any future core series games that does so, especially if we can get Epic Shinies for the first time. Plus, I would love to be able to relive the memory that shot Espeon into the top tiers for me on August 7th, 2019.