Because cleanliness varies. If you make cars public, people will trash them like they do all public transportation, mostly through disinterest. The investment into your own car is a reflection of yourself and something you can take pride in.
I've had roommates before. I just can't do that again.
Why not community owned laptops?
For the near future, company owned cars or even privately owned cars that service others seem reasonable. There's an incentive for profit and it seems like something that could compete with a normal commute and some other things. So I wouldn't be surprised if that happened.
A little after that, I wouldn't be surprised if these "on demand" cars could be part of public transportation. In a lot of places buses or even trains are hardly profitable, which I think would be a good market and a win-win for everyone involved.
The dividends thing.. I am not so sure of. If the cars were owned by the city, the revenue could be used the same way money from public transportation is used.