If all one is interested in determining the the dollar value of all that has been produced in the economy, then, counting the steel, and other parts of the car along with the car would be double counting. But the dollar value of what has been produced in an economy is, perhaps, the least interesting thing we could know about it.
If we really want to understand an economy, we have to know how all the different resources people have get allocated into all the different production processes. The monetary value of all production tells us nothing about this.
When we begin to investigate the working of the economy we see that consumer demands can only explain the production of consumer goods since consumers do not demand producer goods directly. To explain the production of producers goods, we need to understand entrepreneurial demands for them. When we trace back the production of consumer goods to their sources, then, we see that the amount of demand entrepreneurs have for all the producer goods necessary to make some consumer good far outweigh the demand consumers have for it. In other words, the far great portion of production in an economy is of producer goods, which is explained by entrepreneurial demands, which results in investment spending. Consumer demands and consumption spending are a far smaller portion of all demands and total spending and the production of consumer goods is a smaller portion of the production across the entire economy.
Murray Rothbard explained all of this and why it’s important in the production chapters in Man, Economy, and State: