The more I think about it, the more I like this metaphor. Because you CAN make SOME estimates based on what's in the closet. If it's a huge closet, you could guess that the house was fairly large. If there are a lot of coats of different styles, you might infer that many people live in this house. But you're still making a guess about something you can't actually see because you haven't been given enough information. Brilliant!
The problem is no one has locked you in the closet - just open the door and look around. Heck, you have a whole hour to look around the house and estimate how long it takes to build the thing.
You are limited by how long you can spend inspecting every nook and cranny of something, but you're only limited by time. The "door" metaphor is misleading. Nothing is standing in your way from exploring the space.
If you can find the "hard parts" of the house faster than someone else, you're likely to be a better estimator. In fact, my favorite trick is to focus on one hard part and extrapolate up. For example, write down how tricky it is to build the kitchen, or heck just a cabinet in the kitchen, so everyone gets it when you say "oh, by the way, there are 10 more rooms."
At Bigco, you can't start opening doors until you give them your estimate and get it approved. There's no way to know how many more doors in how many more rooms there will be until you've been in all the rooms and opened all of the doors.
Its fractal. That "last" door could lead to 100 more. Oh and its almost always a horror flick with axe wielding maniacs(1) and booby traps(2) in each room intent on your destruction.
(1) The boss's boss's nephew who's a "computer whiz".
(2) $300,000 "developer tools" you have to use by fiat policy because, dammit, we spent a lot of money on them.
Knock on the walls, scream and see if anyone hears you, listen for sounds through the walls, if you do this for enough houses before you got a chance to open the door and walk around you might be able to make order of magnitude estimates. Always assume the house is bigger than you think.