I think you are underestimating the number of people who would need the actual car unless it's extremely feasible to rent one for 6 hrs.
For day to things yes what you say makes sense.
But there will always be times for almost everyone where you need to go somewhere that's not quite far enough to fly and not close enough to use public.
And if you do rent there would be a lot of 1 way trips.
Say you go somewhere that is 6 hrs away but you are going to stay there for several days.
I guess In that situation the rental car would drive back to its original location empty .
Or maybe a large national company would have holding stations for these types of trips.
Say you leave New York to Chicago but you will stay in Chicago for 5 days.
You can use other transportation once you reach Chicago.
Instead of the vehicle driving all the way back to New York it can stay at a holding station owned by the same company to be used for someone in Chicago .
Very interesting but I do think many people would need to outright own the vehicle .
There would be fleets in every major city for city to city transport I'd imagine. Maybe a new company emerges or maybe a company like Avis steps up and fills this role. Keep in mind families could possibly own 1 car instead of 2, 2 instead of 3 or 4, etc. Doesn't have to be 1 to 0.
If you're going to start coming up with scenarios where it won't work, you'll be able to comeup with more than a few. The main point is there are also more than a few where it will clearly work and will be a no brainer in terms of both economics and convenience.
Obviously it would take awhile to be feasible for every single aspect of transportation but just a 20-30% market penetration rate would have a major impact.