We can just wait for this problem to go away as robocars becomes the norm. We'll look back on the primitive times when kids couldn't just click a button or whisper an instruction for a ride like anyone else.
I live in a well-to-do community where many kids are chauffeured to school. The problem isn't just the parents' wasted time. It's the congestion and lack of agency this behaviour bestows on children. Head to head, I'd bet the kid who can navigate themselves to and from school outcompetes the one chauffered in a robotaxi in novel environments.
It really is a mental problem more than anything else. The inability to imagine a virtuous public realm welcoming to children, conjure its value in one's mind eye, and commit to the necessary material changes.
If it has to be techy-flashy, would it satisfy you if the bus was self-driving?
We can walk to school and see the bus when we leave the house and easily beat it by many minutes.
(Busses being slow and routes taking long is probably a design feature, allowing schools to let out at 3PM but parents to not have to be home until 5PM or later).
But the real final solution won't be robocars, it'll be robokids. Then if you lose one you can just get a replacement.
Though you are correct a bus is slow, done right they are faster than walking.