So there needs to be competition between sellers of a single brand, just because some people are so brand-loyal that they would refuse to switch brands to avoid being 'taken to the cleaners?' I'm not sure I agree with this sentiment.

You're also ignoring that the brand (e.g. Chevy) is selling to all of the dealerships. If they raise the price, the dealerships all have to pay if they want the car/truck/etc. Do the dealerships really have that much bargaining power?