Of course if you’re thinking in terms of “broadcast internet” with a Facebook at its center you may be correct
There is still a difference between cache and what's on hard disk.
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
A lot of email clients also have support inbuilt. (Thunderbird, Outlook, and others).
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.