Except that our experience shows that over time competition decreases and things like regulatory capture happen so it becomes harder for anyone small to enter into competition and then prices get hiked up.
And the cars and autonomous driving software itself is becoming more expensive and more subscription-based over time so those rents are going to have to be passed on to the consumer. Large autonomous taxi services may be able to strike better deals or even build their own software/vehicles if they're big enough, but you're not going to be able to compete with them effectively by purchasing a Tesla (and presumably consumer prices will rise as there's less individual-owned vehicles and companies go seeking after only the highest margins and abandon the toyota-corolla market to the robotaxi corporations).
Uber tries that, but it turns out in many places you can't offer human-driven taxis much cheaper once you put them on equal footing regarding insurance and other relevant regulations and stop running the service at a loss.
Most traffic occurs during the morning and evening commute, you'll need roughly the same number of vehicles for those surges unless those norms change as well.
They can, but nobody wants a ride except drunks. Which is one reason why taxis look so bad: when a significant portion of your clients are drunk (throwing up in the back, peeing on the seats and all the other things they do) you don't want a nice car. Nice taxis don't work those shifts. If there is a big shared car market (I doubt it) you will see cars for different times of the day as a profile for potential drunk rider.