"BUT WHY WHY WHY WOULDN'T VW PUT A TEMP SENSOR ON THE ENGINE, INSTEAD OF IN
THE COOLANT???? "

I might be wrong, but I believe just about every car has it's gauge sensor in the coolant.  In fact, most (all) of the sensors are called "coolant temperature sensors".  Not trying to be a smarty pants, that's just my understanding.

Greg, I feel your pain, you did pay attention to the light, saw nothing obvious, paid attention to the temp gauge, but unfortunately something was wrong and then it went all the way bad very quickly.   Hopefully your post will provide a lesson to many, you can't trust the temp gauge, when the coolant has dropped too low to be monitored - in any car!

John