And the obvious answer to that is the characters do not and basically cannot exist in such an information-rich environment. The player's desire for precise metagame information is at odds with the amount and quality of information reasonably available to the character in the fiction. No monster living in a dungeon is going to paint 5ft markings across the floor, for example.
The only time a character would know precisely how far away something is is if they happen to be in their home and happened to have measured the distances precisely before combat for some reason. And then, it's not going to be precise. You might know the couch is 40-some inches and the door's a little smaller than that. But unless you've taken a tape measure to your living room, and memorized those numbers, and can recall those numbers perfectly in a life-and-death situation, you're not going to know exactly how far something is from you. The further from those ideal conditions you are, the less precise your information will be.
You're in a dimly-lit dungeon 100ft underground some 200 miles from your home. There's about a 0% chance of you knowing exactly how far away is that drooling monster who wants to eat your face.
No, we referees should be more honest and prepare the setting in an honest way. As above, unless the conditions are literally perfect, the characters will not have precise information. That the players decide that's not enough, that's cheating, that's not fair, etc is 100% on them. That the players want more information to make a split-second decision than hours worth of scans and measurements could possibly provide is not reasonable and referees should not cater to that.
What a self-contradictory statement. Trying to find out what's going on is acting on the setting. Do you want to know what's behind that door? Guess what, you have to go over there and open it. To gain information you have to act on the environment.
ETA: Try this experiment. No need to report the results. Grab a small cup or bowl and a tape measure or ruler. Go into the biggest room of your home, keeping your eyes on the floor. Don't bump into anything, but don't scan the room. Pick a relatively centered spot and put down the cup/bowl and tape measure between your feet. Close your eyes and stand up straight. Angle your self about 5-10 degrees off-center from the walls. Now...point out your arm at some small object in the room, against the walls, or on the walls, like a TV or picture. Say out loud the number of feet you are away from that object. Open your eyes and look. Now, be honest. I bet you were close, but not spot on with your directions. Now measure the distance from the cup/bowl to the object you picked. Again, be honest. I bet you were off by more than a little bit. And that's the objects in a room you regularly interact with. Now extrapolate that out to a place you've never been before, in less than ideal conditions, in dim light, and knowing your life is in jeopardy. There's no chance you're going to have perfect knowledge of relative distances.