Thinking about this even more, let's just completely disregard Greedy Dice from this picture. Jirachi Prism Star and Peonia will be a two card combo that pretty much any aggro deck could fit in to take an extra prize for a turn. They're both easily searched, since you can just Quick Ball or Ultra Ball for Jirachi and Tapu Lele-GX. Also, since Peonia goes into the discard pile instead of the prizes like Gladion, you can get it back with VS Seeker, potentially doing it again (though you'd also need Scoop Up Net and not every Expanded deck plays Scoop Up Net). But honestly though, you won't even need Scoop Up Net, as all you need is just one turn of taking an extra prize with Jirachi to swing the game in your favor. I could genuinely see this combo being a problem.I've been thinking about this for a while and cannot see how this idea could ever be consistent enough to be a real problem. Adding Greedy Dice to your deck, much less 4 of them, really hurts your consistency as Greedy Dice doesn't actually do anything, it'll be a dead draw a lot of the time. And then Greedy Dice itself isn't reliable at all, if one of them fails, the rest fail. It feels exactly as reliable as Missing Clover was. I think that if you actually manage to win a game with Greedy Dice, you deserve it.
And if it does actually prove to be a problem, then I think there's a better argument for banning Greedy Dice than there is for banning Peonia.
However, I definitely don't want Peonia getting banned. Being able to store cards in the prizes for later is huge, and could actually open up a brand new era of Expanded where we can use prize cards as a resource. Imagine, you use Peonia, put a Professor's Research (or any card you want for next turn) into your prizes while taking what you need out of the prizes, taking a KO and then grabbing the Professor's Research for next turn. That's so good, and opens up a bunch of new plays for the game. I will be severely disappointed if Peonia gets banned, if anything Jirachi Prism Star should be the banned card here.