There would be some markup so the owning company has a profit margin, but the higher the price is, the greater the incentive for competitors to exist, which would exert downward pressure. So maybe you'd end up paying 1/20 the price of owning a car.
If you don't agree, why not?
If I used Uber every time I’ve used her corolla in the past 10 years it would far outweigh the cost of gas, insurance, and fixing the car.
Uber pool is cheaper but why would I inconvenience myself so much for a 2 miles radius.
When people learn they have to pay for cleaning/repairs if they don't take care of the car then they will be much more careful keeping it clean.
Even in the best case, there are lot more people who want to get around during "rush hour" than the rest of the day, so most shared cars could at most work for 2-3 people each day. The types of people who are on the road during not rush hour are more likely to have a larger group (kids) with them so the shared car needed for them is a different size.