>>Why should transportation be different?
Good question, and for many it will not be, and rentals are acceptable.
But also for many, renting a car has a huge ICK factor. It is one thing while traveling to rent from an agency who has (purportedly) thoroughly cleaned and inspected the car before you get it. It would be quite another to rent cars like scooters, where the previous user likely smoked, left wrappers and food debris, and who knows what else, even damage. Plus, most people who own cars keep a fair amount of stuff in the car for their specific convenience, and have their own settings, etc.
The fact that the likes of Zipcar, Turo, and the lot have not entirely taken over urban transport but instead remain niche players shows the extent of this preference.
For suburban and rural markets, it just gets more extreme. How quickly could a rental service be able to deliver a car; could it reliably do it in less than 5-10 minutes for people to run an errand? If not, unless they are insanely cheap, ppl will likely want to own their own. Perhaps it'll be more of a hybrid, households owning one car and renting the spare for specific trips?