(I work for an auto manufacturer, but my opinions are my own. And my lifestyle is my own, and doesn't reflect 100% of slashdot).
1. Peak demand. In car-culture areas there's a peak demand. *Someone* has to own the rush hour fleet. But no business is going to want to invest in a fleet that has 21 hours of downtime during non-peak loads.
2. Consumers want reliability and 100% availability. Consider Uber and Lyft that promise this, except during surge pricing periods. People hate this. It's economically correct in the case of Uber and Lyft, and an obvious idea, but surge pricing during rush hour isn't going to work. People will still own their own cars.
3. Personalization and customization. Hey, I like my cars stock, but I still have my stuff in the center console, my presets on the stereo (yes, 760 am in the morning, I'm a dying breed), and my iPhone paired to Sync. A different car every day isn't going to cut it. And think about comfort, especially on a commute. If it's hit or miss as far as comfort, people are willing to pay for 100% access to a Fusion versus an Elantra (or choose an Elantra versus a smaller B-sized car).
4. Toy haulers. You're not going to call Uber or Lyft to tow your trailer to a state park or tow your boat to a launch. And this isn't 99%'er speaking, this is blue collar worker in my part of the country.
Will annual sales go down? Yeah, probably. Maybe undoubtably (how's that for hedging?). But families in most areas are still going to continue to own their own cars. Maybe not two or three cars -- supplemented by autonomous vehicles or ride sharing -- but the private market most definitely won't dry up, even amongst the 99%.
I'm limiting my projections here to about 50 years. Beyond that, who knows. Most of us will be dead then, so it's good enough.