I would argue it is not an exaggeration. The bans always start small, because they can get away with the small things. And then it becomes normalized and it always escalates if left unchecked.

A small fight over a few books is a much easier fight to win before it becomes the systematic norm.

And yes, libraries have a ton of other services... for now. Do you think these same lunatics are going to leave the library alone after they've gotten rid of the books they don't agree with? After the book bans, will they still be offering free internet that isn't censored? Will they still have information for outreach programs that help homeless people, LBGTQ+ folks, people with mental health problems, and assistance for other vulnerable minority groups?

If they are allowed to have their way, they'll gut all of the services people use, then when nobody is going to the library, they'll have the excuse they've wanted all along to shut it down entirely.

This isn't hypothetical what-if-ism. It's happened before.