doesn't answer the question, why should Tesla be granted an exception not available to other automakers? Chrysler has had all sorts of problems with franchise law in California in regards to operating their own.
From a different perspective, what's wrong with car manufacturers operating their own dealerships? (I'm curious: there very well may be a down side, but I haven't thought of it yet.)
Early on, cars were sold by local dealers. Later, when manufacturers wanted to sell direct they learned that local politicians cared more about the business down the street than some giant company in Detroit. Therefore, all manner of state and local laws got passed to protect dealerships' turf.
In a lot of ways, car dealerships are perfectly suited to exercise power in state legislatures. No matter what poduck district a state lawmaker comes from there are probably several car dealers there. They're often some of the most locally famous people thanks to the amount of advertising their businesses do. I couldn't name my gradeschool teacher from 30 years ago but I sure could tell you who owned the largest car dealership in the area... and sing his radio jingle.
By contrast, few state lawmakers have a Ford or GM plant in their district.