The model workflow of development to staging to production is obviously tried, tested and trusted; but in my opinion is too much management for WordPress.
I still see the need for a staging site for testing frequent WordPress Core and plugin updates (and testing that these two kinds of update don’t conflict or cause breakages), but this is still a two step process. Unlike enterprise level CMS, this isn’t a case of pushing updates out from one platform to multiple locations – these updates would have to be done on staging and production. Staging becomes literally just a testing ground before applying updates to a production site.
Another huge difference is the content management. Writing pages and posts on staging wouldn’t have any advantage. Copying it over to production would almost be easier by doing it manually! Plugins like Curator can work in a pinch, but after the post publishes updates are not pushed up the the parent if they are made. By default WordPress allows for previewing drafts which essentially creates staged versions of content before it goes live.
If a client has concerns about a post accidentally going live prematurely I suggest creating user accounts with roles of Author for content creation. The Author role could then be limited from publishing content, and an Editor could make that final push.
Essentially I see a need for Staging / Production sites, but purely to test updates and new functionality.