This is fascinating. I have a hard time wrapping my head around how this is supposed to work though. Does this assumption never break down at any point? From the moment the iron is extracted and melted to the moment the knife comes into your hand... is there some kind of chain of custody certificate that says it's never touched anything impermissible? Are there entire kosher industries and factories I'm not aware of for making utensils and such?

The point is being simplified. Simply washing a knife will not make it suitable for preparation of kosher food; but there are methods that will.

Searching for "libun gamur" and "hagalah" will provide a starting point for the genuinely interested.

Oh wow I see, thanks, just Googled. For anyone else wondering, it depends, but you need to e.g. heat the utensil to get it red hot!

A brand new utensil is assumed to be kosher, since it's unlikely a factory is going to have food in it that would contact the utensils.

Also, a utensil is koshered by the same heat-level that made it non-kosher. So if used on a fire, it's koshered on a fire. If used only in hot water, then it's koshered in hot water.

It can get more complicated: Some things (like plastic, or wood) can never be koshered (except by removing a layer from the surface, for example by sanding) because they absorb too easily.

Red hot heat can kosher anything, but those substances can not withstand the necessary temperature.

Glass is interesting as it's considered impervious, and some hold that simply washing it is enough because nothing absorbs into glass.