Many universities are eager for bright students to enroll in their honors colleges. These honors colleges allow the schools to be open to a large segment of the population while providing an elite, or at least semi-elite, education to the brightest students. Having these brilliant students on campus elevates the level of scholarship for the entire campus, so I would think this is something the universities would want to subsidize.
And in fact some do. I know Ole Miss and Alabama give very generous merit aid for high ACT scores. Ole Miss will usually tack on additional aid for honors college participants, and I think many other schools will as well.
My wife graduated with honors from Vandy, and her diploma states that she graduated with honors. Of COURSE she would list this on any job application. This is even more relevant for some of the flagships with low admission standards, where attending the honors college is a bit like attending an elite university. Why in the world would one not list that on their resume?