This is not what most public libraries do with donation books. They mostly just recycle them.

The very act of cataloging donation books takes a huge amount of resources that the collection managers don’t have.

Many public libraries don’t have a collection management department at all! They outsource that function entirely to vendors and those vendors mostly source new books and spend resources preparing them for the hard use of a library (changing bindings, uploading and cleaning metadata, tagging, etc).

Decommissioning is done by volunteers who just look at the condition of books and chuck the bad looking ones in a bin for recycling.

My wife worked in this industry on the vendor side, your model of public libraries is closer to a small subset of certain big city libraries narrowed to their rare and research departments. The median book bought by a library is a Danielle Steele romance novel packaged for library consumption and sent to a small town library system that will be lucky to have a single professional librarian for the whole system.