You seem to have misunderstood the idea of fair use. Fair use is a specific doctrine covering the acceptable ("fair") use of copyrighted works. Fair use of a non-copyrightable work would be, technically speaking, a contradiction in terms.
See, for example, the US copyright office's explanation: https://www.copyright.gov/fair-use/more-info.html The first sentence is "Fair use is a legal doctrine that promotes freedom of expression by permitting the unlicensed use of copyright-protected works in certain circumstances."
Furthermore, there is no requirement that fair use be non-commercial. It is more likely that the courts will find that non-commercial use is fair, but that is not a hard and fast rule. An easy example here is book reviews quoting passages from the text.