I still don't understand why it requires a browser plugin at all. I find it very suspicious and it put me off Feedly.
This, totally. They basically have to make a custom app for every platform/browser, when a single responsive website would have done the trick. I really don't understand the rationale here. What does a plugin platform give them that a simple website does not, if not additional tracking behavior? Does their monetization strategy involve selling data?
Actually creating an add-on allowed a lot more than offering a simple web-site. Remember Feedly is not new, it's been out there for years. Back then, offering an add-on allowed them to lower the stress on their platform by allowing most of the network trafic to be directly between your browser and google's servers. Now they have migrated on their own Cloud platform, they will probably very soon offer a plain site version without the need for add-ons.
"They basically have to make a custom app for every platform/browser, when a single responsive website would have done the trick" ... well their are 2 things there: packaging add-ons for multiple platforms is not difficult. You create some kind of packaging wrapper code around a common codebase. It's building a codebase which works on many javascript and DOM engines that takes time and effort. So building a "responsive website" (that works on most browsers) is not much "easier" than packaging custom app for each browser.