This is really useful thread. I have always battled with use cases for brochure sites, despite totally espousing the use of UML... I often feel caught between UX agency outputs & trying to ensure the whole Requirements Spec ties together, especially when agencies tend not to use UML.
There are several use cases that do apply beyond view menu / view brochure page - site functionality like print page, search site etc, sometimes accept a cookie to view specific content - but not much on classic brochure-ware. (All that ties well into user journeys / personas without having to restate the UX deliverables)
However, once using a system eg a CMS to create the website content - then I think the use cases get properly useful (as per comments above), as there are not only (usually) several actors inc the system, but also varying cases per content type so you can reference those UX deliverables without duplication and start filling in the gaps, plus tie up content strategy type deliverables (eg workflow & governance) by looking into the business processes and the system / user interactions. At the end of the modelling & specifications, you can get useful test matrices this way; plus class diagrams that relate objects to taxonomies (more agency deliverables to tie together in Functional Rqmts / Specs stage).
That's the way I'm trying to tackle it these days.