It appears that Apple may be working on adding service workers support to WebKit. The Register recently reported that the WebKit Feature Status webpage now shows that Service Workers is currently "In Development." This change in status comes shortly after Greg Blass, a Philadelphia-based web developer, posted an article on Medium criticizing Apple for not supporting progressive web apps via service workers. The article has received quite a bit of attention, particularly on Twitter, which may have helped draw Apple's attention.
Google describes Web Service workers in a Web Fundamentals article as "Rich offline experiences, periodic background syncs, push notifications—functionality that would normally require a native application—are coming to the web. Service workers provide the technical foundation that all these features rely on."
Google has been supporting PWA technology for a while, and Chrome for Android includes service workers support. The WebKit feature status for service workers was "Under Consideration" for some time before the recent change in status to "In Development." Based on recent Twitter posts, many developers will be happy to see Apple add service workers support to WebKit.