Can't taxis already operate 24hrs a day? Just rotate out the drivers.

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.

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.