Our library is trying to set some parameters around what we require from a patron in order to check out library materials to them. For adults and teens, this is straightforward: we require they have their library card or a form of identification.
First, I'll answer the easy question: No, you are not overthinking this.
For children fortunate enough to be brought to the public library at a young age, the experience is life-altering. They grow as readers and thinkers. They see themselves as part of a community that shares resources. They start to absorb the values of privacy and information access.