How/why would a production car need to process it differently and why couldn't all processing be done in real time? Safety certification means the car's functionality has to be static, until the next certified software update. Data does not need to leave the car, since the purpose of the data is for the car to drive, which is a transient state.
The technology needs improvements, and the process of making those improvements is hungry for data. Every manufacturer will be in development/debug mode of their self-driving systems at least for the coming decade, so sensor data from every mile of every car is wanted and useful, and manufacturers are configuring production cars to upload as much raw sensor data as is practical.
Each society can decide whether to permit this particular product to collect unlimited data. The presumption is that the data belongs to no one. Let's see what happens when more than one large corporate entity lays competing claim to the same data subset, embedded by a wide-ranging data dragnet.
A 24/7 data feed from your toaster is not going to make your toaster better. It might help an R&D department identify some ways how the next toaster model should be different, but that's about it.
However, a self driving car is data-starved and is still going to be data-starved years from now. At any moment of time, your car could drive better and safer simply if it had more "experience" - the v1.24 software release can be meaningfully better than the v1.23 software release even if R&D department does nothing else but simply import the data received from millions of other cars; if your car is allowed to learn from what other cars saw.
Ensuring that the quality of driving systems increases as fast as it can is important for the society, with a major impact on injuries and casualties. I feel that it would be best for the society if we ensure that this learning (and the required data transfer) is not prohibited, as long as we can solve/restrict the potentially harmful uses of the data.
We don't actually know that self-driving cars are possible in unrestricted environments. The industry is asking for highly invasive surveillance but has no liability for failure to deliver. What happens if "more data" turns out to be insufficient? Will the next request be "restrict the environmental context" or "pass new laws to change human behavior"? Where does it end? Other industries have to deliver results before changing the market. Uber et al promised the moon to their investors, then ignored local laws, then promise to save lives, then ignore privacy concerns, then ..?