the answer, which sounds snobbish, is that no one reads the books. there's like a whole cottage industry on youtube answering lotr questions that are explicitly answered in the books by characters. and i'm not judging, i love those videos, that's just the reason why.

like with the flying nazgul, the movies establish they can fly, but the books establish this fact way more saliently, and also heavily emphasize the characters' obsessive need for secrecy due to mordor being all over the place. so you don't really think that flying is an option for them.