I would think an old worn lock would tend to accept a slightly miscut key more than a new lock. I wish I could have found a local to hand cut me a key, but I had no key at all. I burnished mine on a wire wheel ( grinder ) Hopefully, Govnuks parts, who made my key, will make me another that is symmetrical, which I can duplicate locally.
As to flipping a key over in the machine, I made keys in the old days with a simple machine. Those days are gone. Now, Home Depot, and Ace Hardware, etc. have the self service idiot machines, requiring little or no knowlege or training. Corporate does not give a damn if the key works or not. They see a bad key as "guaranteeing you to return to the store", where you hopefully will buy a $3.00 Gatorade, or a cheap Chinease trinket. Customer service and technical expertise are Nostalgic concepts, becoming extinct by corporate and stockholder greed.

Society is collapsing but my 401K is doing great!