The biggest advantage of using an RSS reader is that it’s a single place that has content ready for you to consume in a list based interface. The web browser interfaces of websites, on the other hand, have all kinds of crazy and trendy layouts where content is a third class citizen (first class and second class are both reserved for ads). This makes skimming easier and quicker. There’s only one way to skim in an RSS reader regardless of which site’s feed you’re looking at. You don’t have to go through the mental exhaustion of skimming several different website layouts, fonts, colors, etc.
I use a couple of RSS apps across devices, and at least one of them is running all the time to refresh content periodically so that I don’t miss something (I know there are online aggregators, but I haven’t found something that I liked and preferably very cheap too). I don’t try to read all the articles across sources since that’d be an endless effort, not to mention completely wasteful. I skim through, read some, star some for future reference or use and mark the specific source (or all) as read.
One thing I hate about many sites that provide RSS feeds is the lack of full text content in the feed. It’s always a jarring experience to open the link to the full content and experience chaos that’s in complete contrast to the reader experience.
On Mac and iOS, I’d recommend NetNewsWire (free and open source). In the past, I’ve used RSSOwl (cross platform) and Vienna.