Why do they need a "legitimate business need" to access the material? Why aren't they instead requiring a simple library card and/or identification.

That's why people are upset. This is more than just requiring a library card.

> Until some random crazy person exercises the same right and destroys an irreplaceable rare book.

Every library I've been in with rare books requires supervision by the archivist if you want to browse them. Sometimes only the archivist can handle the book.

The fact that these rare books aren't all being destroyed in mass tells me that this system works pretty well at screening crazy people from destroying books (and, frankly, there's not a whole lot of people dedicated to destroying rare books).