You're not quite getting my point.
It's not that it has to simulate reality. It's that a simulation has to simulate something. Anything. For something to be "Verisimiltudinous", the system has to actually inform the narrative. And in D&D, it never does. The system in no way tells you what happens. Combat is the easiest example, but, anything else works as well - skill checks, saving throws, anything. Nothing in the system actually informs the narrative.
If you fail a climb check, what happens? If you are at the bottom of the climb, then nothing happens. You simply do not move. Why did you fail the check? What caused the failure? Who knows? The system tells you nothing. Conversely, if you succeed at the climb check, the system again does nothing to actually inform the narrative. Maybe you found foot and hand holds. Maybe you scrambled up. Maybe fairies came and lifted you higher. Maybe you succeeded by the lightness of your heart. Who knows? Any narrative you choose is equally valid as far as the system goes.
I have no problems with the idea that your players want to feel like they are acting in a real place. I get it. I honestly do. But, I do not understand why you would choose D&D for this. Or why you would think that D&D is providing this in any way, shape or form. D&D, at no point, informs the narrative. Because it is not, again in any form, a simulation of anything.
IOW, your players would feel like they are acting in a real place regardless of system since D&D isn't doing any lifting here at all.