> Because creating a cooling system to use on a body with a central nervous system fighting to keep it warm
And yet, something as simple as ice cold water seems to work fine for this. You can cool e.g. even a heatstroke victim pretty quickly, without worrying too much about internal thermoregulation.
> a central nervous system fighting to keep it warm
A heat stroke victim the body is fighting to cool itself and failing. You assist. That part is easy.
Getting the body to do the opposite of what you want is the hard part. ie. Cool down below basal body temperature, stop breathing to perform thoracic surgery.