[acdha]

That's really a very smart comment – no matter what happens with HTTP/2, things like geographic distance and failover are still going to matter and CDNs will still be important.

One key thing which should make this work is that server push should follow the same origin checks as most other recent web standards:

“All pushed resources are subject to the same-origin policy. As a result, the server cannot push arbitrary third-party content to the client; the server must be authoritative for the provided content.”

(http://chimera.labs.oreilly.com/books/1230000000545/ch12.htm...)

Assuming that survives contact with the actual implementations, you should be able to avoid latency-sensitive content going through the CDN while still being able to push out e.g. stylesheets & referenced fonts/images.