I’m in Florida, third grade. We are required to catalog all of our classroom libraries in a format that can be accessed on the school’s website. At my school, our media specialist has been doing this for us but that isn’t the case at most schools. I have over 1,000 books in my classroom (not all of them out all of the time) so I would’ve been taking my books home had the media specialist not offered to do this for us.
As far as banning books, no.
There is a process for people to object to books in a school library but nothing has been objected to or banned that I’m aware of.
ETA: Actually, I know of one book that parents tried to ban in elementary/middle schools (and I actually agreed with the particular book, Gender Queer, not being for those ages) but it wasn’t even in circulation in anything below high school.