Push tends to be more efficient, and more responsive, for content that updates less frequently than the polling interval.
Of course if you’re thinking in terms of “broadcast internet” with a Facebook at its center you may be correct
So basically WebSub but you don't need to run a WebSub server - you could just parse feeds using, for example, a procmail script. Email is already a well-supported protocol; WebSub is not.
A lot of email clients also have support inbuilt. (Thunderbird, Outlook, and others).
The system works quite well, and I can read my RSS both via a client-side app (thunderbird in my case) and on the go via the webmail. I even made a small modification to rss2email to automatically "tag" the mails so I can use mail filters to automatically sorts the feeds into different folders.
I have a server that fetches the RSS content a few times a day, but I guess it could also work "locally", for example by doing it once each time I turn on my computer (if you are okay with "missing out" sometimes on very active feeds).
I decided to do the switch when I noted that the interfaces of my email client and of my RSS reader were basically indistinguishable.
EDIT: for the anecdote, this project was initially created by the very same Aaron Swartz that, among other things, contributed to the creation of the RSS format http://www.aaronsw.com/weblog/001148
There is still a difference between cache and what's on hard disk.
In AP you don't need to follow anyone to have messages for you delivered directly to your inbox.
You have to check other servers if you're interested in messages to others but I guess there is no analog to that for email.