I think, if your concept is specifically that they should "do something as appealing as shiny Pokémon" (and I'm not sure if it *is* what you mean or if you're just using them as an example for a general concept) then we have different understandings of why those are appealing - and I say this as someone who spent many hours back in Pokémon Silver riding up and down outside Goldenrod City trying to hatch shiny Charmanders!

I wasn't doing that just to see a shiny Charmander, I was doing that because I wanted to own one, or rather the near-legendary black Charizard it would become. That's gameplay with an end goal, more akin to grinding for mounts/minions, just very heavily dependent on RNG to finally achieve it.

The chances are also very different even if you're intending for the same likelihood of it happening, because you're getting that 1-in-8192 chance per encounter rather than per dungeon. Let's estimate, one encounter a minute in the wild, 60 encounters in an hour = 137 hours of play to have 8220 encounters. That's decent odds if you're playing for an hour a day for a few months.

Put those same odds onto something happening in an instanced dungeon. One instance takes four people 15-30 minutes; let's say one hour of collective playtime = 1 dungeon clear. That means (if I'm doing this maths right) you need 8220 hours of playtime, or 2055 hours per person just in instanced dungeons to yield the same chances as that 137 hours of hoping for a shiny.