As a GM, you have a perfect, complete vision of what happened, what is happening, what will probably happen, every character, every event, and, most importantly, what is important and what isn't, and how things are connected
As a player, I just don't know what details I'm supposed to remember. I'll remember only part of an information. I'll mix characters and places. I'll forget the description of the villain. I'll forget that you said there is a red carpet in the bedroom. I'll not pay attention to that long list of titles of the sidhe lord because they're probably not that important, right?
- So I won't randomly ask the GM to repeat the complete description of every NPC in the game, just in case it's important. And I probably won't notice that the Mysterious Stranger I just met fits the description of Lord Alexander Ravenwald that I met last game, unless the GM lays it out really thick, or simply says "That guy really looks familiar, by the way." if it's just a hint to get me thinking and check my notes, or "You can't see his face, but he has those long blue-black hairs of the Ravenwald family" if it's important that I remember.
- And when I say I'm checking the walls for secret doors in the bedroom where someone got murdered, the GM, who knows the red carpet is hiding a trapdoor, could remind me of its existence, either in a new description ("you put the painting down on the red carpet in the middle of the rooom") or simply by asking "do you check under the carpet, too?"
- And when I talk to the seelies, the GM could say "The tall sidhe present himself as the Lord Protector of Muir Wood", or even, if I'm not reacting to that name, "Muir Wood... It takes you a few seconds to realise that it may be the same place that the Dancers are about to attack"
The players hear LOTS of things over the course of the game, but only the GM knows what is important and what is "fluff". Reminding the players of some details they forgot is not playing in their place, it's giving them more options.
If a player looks like an idiot, check if they have the same "mental image" as you. 9 times out of 10, they just misunderstood, didn't remember an important piece of information, or didn't see the link between 2 "obvious" pieces of information.
(Like in you example of the barbarian jumping off a cliff, even if they're aware it's 20D6 damage, they may simply not remember that the "massive damage" rule exists at your table. If you stop to tell them "it will be 20D6 damage. If I roll over 50 damage, you'll have to save or die. Do you jump, or not?", it's not a mistake anymore, but an informed choice)