Network effects. Google Reader was big enough that many websites added RSS support to ensure users would return.

When Google Reader died, too many people stopped subscribing to feeds and hence websites stopped offering them.

I'm afraid it's not a simple feature you can just add to your reader :(

One of the more under-rated features, was that it could turn any site into an RSS feed. So if you had a niche site you enjoyed, but didn't have an rss feed, you could still plug it into Reader and get any new articles as if it had a built in rss feed

I can also vouch for Feedly. I closed my Google account years ago and needed something to track my YouTube subscriptions. I use it for blog RSS feeds too. It's one of the few things I use that works so well that I don't really think about it.