It's really changing the temper of the wire.
Think of a 2 inch piece of solder made of a lead like substance [not really but this will serve the point]
Now think of a 2 inch piece of guitar string.
Bend the solder and it stays bent [Low temper]
Bend the guitar string and it Bounces back to being a straight piece. [High temper].
If you heat that guitar string up to glow red and dunk it in water [cool fast method]
The guitar string will act similar to that piece of solder, it will "Stay Bent" and no longer "Bounce" back to the original shape.
Replace the word "Temper" with "Memory" Some engineers like to use the term memory instead but it's the same thing.
Kanthal wire has a fair amount of Temper [memory] but heating and "RAPID" cooling removes it and makes it take on a character similar to the piece of solder. So if you scrunch the coils or just plain wrap them the Kanthal [or any wire for that matter] will not "ARGUE" with you and stay put instead of bouncing back.
Heating slow and cooling real slow will INCREASE the temper [memory] characteristics of the wire or any metal in general. That’s how they make springs, drill bits etc... This is the opposite of what we are doing in here.
Now that explains temperament. Some people think "Anneal" may mean the willful action of making the surface of the heating coil less conductive so it wont cross short from one coil to the next when they are scrunched [touching] and laying on top of one another. I am assuming that one because I never heard an engineer say "Anneal" the metal to make it lower tempered". They just say "lower the temper".
Last but not least;
Wiki does not mention conductivity however they only mention temperament, molecular structure.
I'd rather use the term "Carbonize" for this electrical insulating procedure, then again I don't subscribe to this It's unreliable , flakey and makes for an "unstable wick to coil mate" in the long run.
Putting a ceramic sheath or Silica rope bra and or cotton wrap between the coil and wick is more my style and it insulates the heat from the coil from wasting energy on warming up your hand and not the juice. saving battery life and running low watts wile achieving the same performance.
This activity is not as common when dealing with plain silica or cotton rope wicks, but more often seen in dealing with metal mesh or wire rope [cable] wicks. I use wire rope [cable] with a thick layer of cotton because I don't trust annealing at all for insulating, I do anneal for lowering the temper of the coil however. I just call it "lowering the temper", "soften it up" and sometimes just say "Heat-Dunk, 3 or 4 times".