I predict that in that world, the buy it today, drive it home tonight makes would capture market share. Honda already does a great job of building just one or two configs (very limited option space, other than color) and sells a lot of cars that way.
In an "Amazon Prime" world, few people want to wait 21 days for their new car is my hunch.
I expect we'll see a mix of both. Dealers will continue to stock the most common configurations, and offer them at a discount. Slightly less common configurations will be stocked at manufacturer regional distribution centers available for delivery in 1 - 2 days. And really rare configurations will have to be custom ordered, with the customer paying full sticker price and waiting much longer. As long as the manufacturer has excess plant capacity in the continental USA and a lean production process it ought to be possible to do custom final assembly and shipping in <2 weeks.
My father sold new cars ~30 years ago and custom orders were actually more common back then. Many dealers and volume manufacturers actively discourage custom orders now, even when customers would be willing to pay more to get exactly what they want. I think this is because of badly aligned incentives and will probably change.
Did rental cars suddenly disappear? After every car accident I was involved in where my car was a total loss, I had to wait 5-10 days for a check from my insurance company to cover the loss. During that time, a rental was provided to me.
In an "Amazon Prime" world, few people want to wait 21 days for their new car is my hunch.