I am just trying to imagine what you need to do to get as close as possible. Maybe I make this a project happen if I end up with something actionable. Maybe these ideas inspire someone else, maybe they fade away into memories and do very little.
I love the it doesn't matter what you choose you can check it out part. I think it would be really important to have a filter where all the books the kid can see, the kid can have right now. This of course could be disabled by older kids that understand sometimes there is a wait but I think for the younger kids this would be an important detail.
I don't want to replace libraries, I want to make it so every kid that has access to the internet on some device or gaming platform can get 30% of that experience. Or whatever is possible.