Typically my kids rode the bus to/from school ... but I can remember times when we had problems. The most frequent issues were in middle school: We had bus service only in the afternoons -- I can't remember why -- and when my husband went out of town, it was a problem for me. I have to be at work before 7:00, kids couldn't be dropped off before a certain time, and it was a solid 30 minute drive to my school. We did various things to make it happen, including dropping them off at a friend's house in the mornings and hiring our teenaged baby sitter to drive the kids to school occasionally.
Would I have trusted an Uber driver (a stranger) to take my middle schooler to school? No, I don't think so. Maybe I'm being conservative about it, but I think 15 is the youngest I'd want the child to ride in essentially a taxi alone.
Riding bikes isn't always an option. For example, our middle school is more than 10 miles from home and the roads aren't bike-friendly. And none of our schools have facilities for securing bikes during the day. We're not a bike-friendly location; you can argue that we'd be smart to live elsewhere, but the real point is that bikes aren't an option for everyone.
I'm also surprised that day care would allow a driver to pick up a kid. When we had a family emergency a couple months ago and I had to go pick up my 4-year old niece, the day care wanted to see my ID and called the child's mother to verify that I wasn't trying to snatch her.
We have LOTS of services for picking kids up from school. When my kids were in elementary school, I know I saw the day care vans/small buses in the parking lot picking up "their kids" -- and my nephew does something like this now; he rides the public school bus to his old day care and his parents pick him up at day care/after school care. A couple churches have after school programs, and those kids are picked up in the church bus. Karate, dance, and gymnastics studios pick up kids on certain days of the week, take them for their activities, and their parents pick them up there.