These ideas sound fine on paper, but for first time visitors (on a warmed up browser), server push didn't show any improvements to page load times in my benchmarks. My question is why enable server push at all?

I am no longer with the company for whom I performed the benchmarks, that's why I can't publish them. Perhaps there are other benchmarks out there, that show server push is more performant. If so, I would be happy to see them.