Over there, taxis refuse going out of city limits or even to remote parts of town where they know they won't have a passenger back. They have reserved spots for parking in many areas (just idle in grey-legal spots). There would be many autonomous cars and they'd follow rules more strictly I guess. So they'd have to drive off to find some parking. Then come back to pick up next customer. They'd drive a shitload of junk miles to pick up/drop off people to suburbs. Taxis either refuse such trips or charge $$$.

Current car sharing service (e.g. zipcar) is virtually the same as autonomous car sharing. You're not removing any large costs. Fleet balance is arguably the only cost removed. But it seems to be more or less solved problem even without autonomous cars. At least in my city, they no longer require to return (most) cars to the same lot. Wether car is autonomous or not, you still have to purchase the vehicle, pay insurance, gas, maintenance... Same price. The only change would be paying for idle car, it could drive back by itself. But user would have to pay for those junk miles. Which may be the same as paying for idling in the long run.

If car sharing service would want to have good availability at any time, they'd have a lot of overhead cars. Which would increase the cost. Otherwise they'd have to have reservations. And we get into a whole can of worms..