Your explanation doesn't really make sense.
Consider: who would benefit most from the removal of these laws? The obvious answer is the General Motors Corporation. They could own their own dealerships, getting better control of customer experience and a bigger cut of the profits. It's not like they're short on capital such that they would be forced to franchise anyway. As the largest automaker in the world for most of the last century, they would get a significantly outsized benefit compared to any competitor.
Now for a rhetorical question. Who has more political power in the U.S: car dealerships in aggregate or General Motors? Answer: General Motors, of course!
Another rhetorical question: Does Tesla have more political power in New Jersey than GM as well, given that the exception was carved out specifically regarding the type of vehicle they produce?
edit: New Jersey is no stranger to economic protectionism. They actually prohibit self-service auto refueling as a jobs program, which would seem to be more threatened by Tesla than car dealerships. I'm not trying to argue that it doesn't exist, just that it doesn't explain what's going on here.