Seemingly all they do is make mobs drop 90% less gold.
Is there some hidden mechanic here? Like, kill a treasure goblin while you have a Greed Shrine active, and Wirts leg drops?
every time you hit something, extra gold drops. I think that’s genuinely all they do, the monsters still drop their normal gold amounts but the amount you get from hitting things is tiny so that’s probably why you thought it reduced gold drops overall
Sometimes they are cursed and give you some extra XP and loot for killing the spawning monsters.
If they are not, then they do nothing 
Speed boost. Useless otherwise.