I used to live in Germany, which had lots of excellent public transit, walking, and cycling. There was still quite a bit of car traffic. If even Germany's public transport isn't enough to eliminate cars, then we should put some effort into improving car transport, in addition to whatever we do with buses and bike lanes.
To that end, I'm not convinced automation will make things worse.
If the kid's school is near the parent's route to work, there's nothing stopping the parent from saving money by taking the kid in the same taxi.
If the kid's school is in the opposite direction, then a separate robotaxi can be more efficient. What matters is total system mileage. If a robotaxi takes the kid, then picks up a commuter starting near the school, then we save the parent's trip from the school back to their starting point.
To that end, I'm not convinced automation will make things worse.
If the kid's school is near the parent's route to work, there's nothing stopping the parent from saving money by taking the kid in the same taxi.
If the kid's school is in the opposite direction, then a separate robotaxi can be more efficient. What matters is total system mileage. If a robotaxi takes the kid, then picks up a commuter starting near the school, then we save the parent's trip from the school back to their starting point.