would love to know some offerings that are over the top gratis. some day I intend to write/host my own, but the site I went to in the reader aftermath has slowly ratcheted up their conversion to paid incentives/demands, and now I can't add new feeds.
If your main goal is "very very free," you can't do better than self-hosted open source stuff, and there's lots of competition there. You could also just run a local app that isn't even a website.
I've personally just been using Feedly's free tier, and it works fine. Every now and then they find a new way to say "hey, what if you paid for Feedly," but it hasn't bothered me too much.