If you're worried about being burned again, there's two good self hosted RSS readers out there:

Tiny Tiny RSS: https://tt-rss.org/gitlab/explore

SelfOSS: http://selfoss.aditu.de/

Both include mobile apps and are open source with web based interfaces and JSON based API's to let you implement your own clients.

And almost all of the RSS web services and apps I have looked at support OPML to import and export your feeds. It is really easy to move between RSS systems with minimal loss.

Nope. What about your archives?

I know that for me having an archive of the feeds is pretty darn important.

I can certainly see that for some (many?) people archives are important. I currently use Feedbin.com, and I have occationally searched for a past story.

Mostly, I bookmark and archive important articles, and use a search engine to find more general more none specific info

Don't forget Newsblur, also OSS and has apps for all the mobile platforms.

Why though? There are alternatives.

I went from Google Reader to Feedly, and I'm quite happy.