The logic is that some parents will happily pay a premium to not have to drive their kids everywhere, but below a certain age they won't entrust them to random Uber drivers.

You seem to think that a driver can't do both Shuddle and Uber, but I don't see why that wouldn't be the case. During peak kid hours, they pick up Shuddle rides. When they don't have those, they do Uber, Lift, delivery, or one of the many other things you can do with a car and a cellphone.