Yes, I'd definitely buy a car this way. Not a house, though. And I did buy my living room furniture this way! We're out here. 
I think this is why we've seen most of the work done in this space (at least with Carvana and some other DR solutions) on used. I know exactly what you're talking about. The customer wouldn't know how to properly apply the incentives, but the rules for how and when incentives can be applied can be programmed. Nonetheless, launching something like this would be infinitely easier to apply to used cars, but it should be working to bring this idea to new cars as quickly as possible. At this point, many manufacturers probably have APIs to help this process.
I laugh at marketers when they take this [very] naive stance. I also resent them for poisoning the well, so to speak. Generally, I don't think marketers really understand the car buying process. It's going to take someone who knows the business to be able to know what to promise.
A lot of people enjoy the car buying process, I agree. I am kind of one of them. Selecting a car is fun and test driving it is fun, but the rest of the process is a drag. But I don't think that's something that can be substantiated just by looking at last year's sales numbers. Surely some percentage of people bought new cars because they enjoy buying new cars, but I think that's low on the list of motivators. And nobody likes getting beaten up in the box, or waiting for eons to get their new car so they can go home.