I think this is the mindset required for this conversation. There is no way to make a library drive a profit, let alone financially self-sufficient. However, the library exists because the city values the externalities, specifically an educated public and reduced crime. For those purposes, libraries are incredibly cost efficient.

The same argument can be made for public grocers. Reducing poverty has cascading effects including better health and lower crime rates.

Well no, because the library is often the sole provider of book lending services and there's no private sector alternative. The same can't be said for grocery stores. To continue your analogy, it would be closer to the government setting up its own streaming service, even though there's netfilx and several other competitors. Even though people hate netflix for its price hikes or whatever, it's unclear how the government can do a better job here than netfilx (or other competitors), aside from strongarming/expropriating rights holders.