That sounds like a nice workflow with Pocket, a tool I've been meaning to try to use (I have the extension setup in my browser but never use it, heh).
That being said I really *don't* see a lot of advantage in that setup except for one thing, which is a limitation of many RSS feeds, and maybe in some ways of the RSS format itself (or at least how it is commonly used): limited content length. Many RSS feeds only give you a snippet of the full content, or content differently formatted than the main website. In these cases having a Pocket version of the (presumably) full content is definitely ideal.
Anyway, I *do* still use RSS quite heavily. I use Feedly, which finally gave me a view close enough to the old Google Reader that I am happy with it, at least on desktop web. I tried the Digg reader and others, but none really "did it" for me. Feedly finally got there and I've stuck with it since, at least a year now (I have a G+ post on my experiments somewhere in my feed history, I can dig it up if anyone is for some reason curious about the details). On mobile (Android) I use GReader free, works great. And honestly I find I can pretty much use it just as that quote describes above, except I do filtering/selection of interesting content somewhat concurrently with reading. I can always save articles for later reading if desired, star them, etc. in my reader app. But I tend to read as I go, for the most part. Works well for me.
So for me RSS is not dead, and I hope it doesn't get killed. Given that the workflow quoted above relies on RSS as the content starting point, and I'm not aware of any other real replacement for it for getting updates from general websites, I don't think then that RSS is going anywhere any time soon. Hopefully... Maybe it's just a matter of finding the right reading tools/methods for you?