This seems to be a popular meme, especially on HN. RSS is not 'demised'. It's still used heavily for podcasts, wordpress (and many other blog sites) expose it, and there are countless mobile and desktop apps for fetching RSS and displaying them. RSS is alive and well, even if Google Reader is no longer a thing. Or is considering that RSS did not replace everything on the internet 'proof' that it is dying?
For me, RSS is by far (still) the best way to access web content.
I've tried some self hosted RSS readers over the years but I've stayed with FreshRSS[1] for the last year. It has been a marvelous experience. Zero trouble, zero administrative burden. Self-hosted bliss. Best of all is the fact that it uses a flat file DB so it can easily be backed up, moved around and migrated. Can not recommend it enough. Also, it's PHP, so works on any cheap shared hosting. That's how I use it.
One of the best things about it is escaping the algorithmically curated feeds.
Every site and service that I wish to follow has an RSS feed, except for Twitter. I use RSS-Bridge[2] (self hosted too) to follow users. RSS-Bridge[2] will give you feeds for just about every service you can think of.
If you don't find a feed for a site, sometimes you just have to dig a little. You learn at which URIs the most commons CMSes presents their Atom/RSS feeds (hello /feed/).