They might not be actual requirements for a blog or a brochure site but it's not totally unreasonable for someone to want their website to work that way. The question is not whether or not an SPA is a good or a bad thing, but whether or not the cost (more code, more complexity, potentially a series of background requests after the initial page load) is worth paying in order to get the benefits.
When either an SPA or a multi-page site is done well most users can't tell which sort of site they're looking at. That should be the goal. Make stuff where the user forgets about the tech. Make a website that just works, that's fast enough for users not to think 'this is a bit slow', and that's coded in a way you can maintain and work on for a long time. If you get those things right then no one can reasonably criticise what you've made no matter how you've made it.