> The engine already existed, our public library system

How good one's library is depends on how well-off the operating local government is. The Imagination Library is more egalitarian because it's often funded at county and state-level, so kids with underfunded libraries get the same level of access as other kids from wealthier zip codes

The intention of this program was to get books in the hands of children, who might not have access to a public library. The books were kept free in order to combat the shame often associated with not being able to afford books for your kids. These two services might be catering to two separate (though sometimes overlapping) audiences.

I think this quote from her sums up the thinking behind it:

"It’s the fact they get recognised. They get this little book with their little name on it in the mail, and they feel special. They start taking pride in themselves, and they know that somebody out there is thinking of them."

While I agree with this, you can't just give money to the public library system and then they start signing up families in birthing center, or mailing books to kids, they don't do that. Giving them more money doesn't automatically change institutional behavior.