I really don't see the point for feed readers anymore now that Twitter, Facebook and social media are the primary ways of sharing out information. Plus, search engines are still the way to go to find what you're looking for.
People want information in a click. I mean, who is going to go to their Feedburner account anymore, login and check the content from a blog post. It's easier to go straight to the blog and read it from there.
I do see the benefit of someone wanting to plug your RSS feed into the side bar of his website or Facebook page. If he thinks his readers would be interested in the content I write, hey -- be my guest.
Plus, your feed on someone else's site is a neat way to keep your content updated automatically without you having to go over to that site and re-submiting your content.