What advantage would that have over what my bank currently offers to kids? How does it address "I don't think he's yet able to keep track of a bank card, much less a smartphone from a company I don't trust."?

How will I, as a parent without a smartphone, manage my kids' account?

FWIW, I live two floors above the main branch in the city for my bank.

I have deep distrust of anything like frequent flier miles and store memberships as I know they are bribing me with my own money and/or building up a persona to try and sell me more, so seeing "RevPoints" marketing on their home page triggers alarm bells in my head. It means they are building on a system which is already extracting too much money from customers, so we need stronger regulations limiting the excess overhead.