Just wrote an article on Medium about how a (potential) client's site they've loaded up on trickery to try and compensate for their bloated code spread out over several dozen files. In trying to diagnose it and build up a proposal/contract, I noticed that their PUSH was acting funky. It was only triggering intermittently, and when it WASN'T working the pages were faster.
Delta Alpha Foxtrot Uniform Quebec.
You can find my findings in the article:https://levelup.gitconnected.com/http-2-push-fact-fiction-placebo-746cee7e3bdf
Though to summarize, Push was not slowing the site down "really", it was just making deeper rooted issues worse... but when I made a synthetic test, I found that in general a slight push is ok, a giant push introduces problems, and overall what little benefit it actually makes is more related to if your code is bloated BS or not.
It may in fact be a placebo and/or be useless if you just write minimalist code in the first place. A shame since I've been a advocate for it, because I've advocated reducing the total file counts/handshakes as a way to speed up websites for decades.
I don't like this conclusion, but right now the facts in front of me say HTTP 2 push is more placebo than fact; at least for how I build websites.