To be fair, its more that you are operating it unsafely then it is inherently unsafe. Once you know its broken and continue to run it anyway it changes from bad design to operator error.
Its a 20 amp motor your running, which is 240 watts of power flowing through there. Go find a 200 watt halogen and see how much heat that puts off. The difference you were seeing between your setting and its speed seems to have been absorbed by your dash plastic.
Its a little surprising you didn't blow a fuse with the melting like that, but it was apparently creating its own. This is why you don't continue to operate something, especially a relatively high power electric thing, when you know its faulty. There have been many a car fire from things like this.
The design is a bit archaic. They run the juice through a bank of resistors to lower the speed of the blower motor. Difference betwwen low power and high power? You burning off x watts of heat with a bunch of resistors. Theres a PWM mod for this that brings it up to date.
Get that thing replaced instead of messing with your damaged one.