Not going to matter much whether the excess cars for peak demand are privately owned or owned by Tesla. A car in the available fleet is a car in the available fleet. In the short run, there won't be enough robotaxi to meet demand. In the long run, most people will give up private ownership entirely.

There are also going to be many ways to keep vehicles busy other than regular passenger transport, such as doing delivery work overnite, people sleeping in cars overnite for long distance drives, etc.

The low cost, convenience & logistics automation will radically alter the entire demand landscape for personal transportation, shipping & delivery. Part of the impact will be smoothing out the peaks of "rush hour".

For example, a convenient automated ride-share network can make coordinating car-pooling easier for commuters (and much cheaper, splitting the ride), thus drastically cutting # of cars needed (I'd say as few as 1/4 as many cars needed). An automated ride-share network can adapt instantly to car-pool requests, minute by minute--you don't have to have a group of 4 coworkers who liver near each other and carpool on a specific schedule every day.

Also, the very nature of work is changing, such that "rush hour" will tend to be going away anyway over the next decade or so.

The logistics AI that manages the fleet will find the best ways to preposition & utilize vehicles, and plan the right mix of different size/types. I think we are probably underestimating if we think most robo-vehicles will only average 8-10 hours/day of productive utilization. I think in the long run it will be double that, 16-20 hours/day.