Huh, that seems weird to me. _Obviously_ push would go almost nowhere in 5 years. Hell, HTTP/2 itself is still extremely new. Server push requires people to totally redesign how their infrastructure works, because their web server needs knowledge about the application.
I would expect server push to be basically unused until something comes around to automate it. It seems totally plausible to me, for example, that NGINX might add some logic to automatically keep track of which resources are requested after which other resources, and, for example, notice that "/style.css" is requested after "/" 99.9% of the time, and therefore automatically push the stylesheet.
It says a lot about Google if their approach to this stuff is to build something which requires the entire world of web servers to adapt, and then rip out the feature if it doesn't take off right away. If they were serious about it, getting everyone to restructure how their infrastructure works should've been treated as a decades-long project.
This just reinforces my existing view of not trusting Google for anything important. They just can't keep at a project. Imagine being the sucker who suggested that a business should spend a load of time restructuring their back-end infrastructure to support server push, just for Google to rip it out.