Now I don't have to check anything these days, except my email, which of course I check everyday anyhow!
Moreover, one of the great benefits of RSS is that it is customizable and one's reading experience pertains specifically and only to them. With newsletters, one is throwing their reading experience to the mercy of the newsletter editor. This is not to say that newsletters aren't valuable. Their spontaneity and conciseness provides a great reading experience. (Although, I think Twitter is superior at this type of thing anyway.)
But, given the idiosyncrasies of newsletters, I just don't believe that they are tenable alternatives to RSS. Those who want to read a lot of content from an eclectic array of specific sources still need something like RSS.
With newsletters, one is throwing their reading experience to the mercy of the newsletter editor.
This is part of the appeal for many non-power readers. The majority are not particularly interested in curating or even controlling their sources and are happy to outsource it to either trusted editors (see almost the entire print media or something like Techmeme) or the "cloud" (e.g. Reddit or Hacker News).
For my part, it's a lot of browsing, including places like Hacker News and Reddit, and notably a lot of great things get submitted to HN but never get any votes.. those are always the coolest finds. There are also a lot of Twitter users to follow who produce content and tweet about it. I also get a lot of direct e-mails from people who create things, perhaps a third of links come via outreach from authors.. but that's the sort of thing that only happens after you've been doing it a while.