This is the problem with the permission systems on most newer platforms. It's either all or nothing; Run or don't run. If i find a good app for android where only a minimal feature requires some privacy intruding permission i can't install it at all even though i never want to use that feature. Same on Windows, either it's admin or it's not, there is no middle ground. Most installers ask for full super mega admin permission just to get write permisson in %programfiles%, what if i don't even want to install it there.
I think .NET and Java programs can be run until they encounter permission requirements and then prompt but i have rarely seen this feature used.
Obviously it's a usability tradeoff and the programmers of the app would also have to handle the permission rejection gracefully while running but i don't think that's too much to ask for.
Not sure about .NET, but you have to prompt at load for Java. Your app can continue to run in a degraded manner if permissions are not granted however.
Anyway, this is why it's a shame Feedly doesn't offer a non-extension version. One would hope it's something they have planned. Offer the extension for those who want the additional features and are ok with the permissions, and the web app for the rest (and for the convenience of access anywhere, cross-platform).
"Why does my RSS reader need access to the webpage to add the RSS feed for that webpage?"