I've been told the inducer motor on my Goodman furnace has burned out because 'the cooling fan is missing". Does anyone know if this is a legit diagnosis? I didn't even know there was a cooling fan for the inducer motor on furnaces.

Many times there is a small fan that blows over the small motor to help keep it cool. It is attached to the motor it is cooling in most cases it is external but I have seen internal ones also.