Purpose of a spiral/wound copper wire in a DC motor?
That looks like a Behr blower motor as used in BMW etc. 

The coils are inductors (wire wrapped around a ferrite rod core) for EMI filtering so the fan motor won't muck up the AM radio reception etc. 

Brushed motors are used because they are cheaper (including the controller). Life is not really a big deal in cars- figure if the average speed is 30mph and the car lasts 60,000 miles for the original owner, that's only 2000 hours of operation, and the fan may not be used for all of that. 

My experience is that they last around 100,000 km (60,000 miles) on average.