Wouldn't this remove the whole game? Everyone would pretty much know whether the dungeon is survivable and it would often come down to the last person deciding whether to let the someone win or taking one for the team and getting killed.
Try the rules as written. It's a whole lot of "Why did they remove that? Do they know something?! I do know there's a demon, but what if there's also a dragon?! Maybe I can trick him into going into the dungeon!"
Monsters are only placed face-up when they're used to remove an Equipment. Otherwise, they're placed in the Dungeon face-down as normal. You still don't know what other players put in, so there's still ambiguity as to who knows what and why a certain Equipment was removed.