I'm speaking from my own experience running Feedity - https://feedity.com, a growing startup that helps with custom feeds for unstructured sources like webpages.
(RSS is, like, objectively the best way to follow multiple webcomics. I don't understand why it's not more popular.)
1. You miss out on the aesthetics each comic's website brings to the table
2. Sometimes you miss things like "hidden panels" or blog posts you're interested in.
3. No advertisement money going towards the artists (Not a big deal if you support them by buying merch and the comics don't need a lot of bandwidth)
I would really love to develop a reader that focused on webcomics, having both a dynamically curated section as well as all of your subscribed comics. Newspaper-like layout. Customized borders around each comic to add back some of the flair each comic's website offers. Quick links to the artist's blog/website/comic permalink. Text/image-only advertisements interleaved between comics, with 100% revenue going back to artists. Even merch advertisements which occasionally appear under an artist's comic, offering links to their storefronts.
Basically an open source Funny Papers for the web, which would offer content discovery for artists through its curated/related sections, as well as revenue from advertisements. It would update daily and could be used to follow both new and old comics serially.
I just need someone to help me build it because I'm juggling too many things to devote all of my attention to it.
The way I use my RSS reader is that I scroll through the list of posts, and if it's something I wish to check back on later, I press the shortcut to send it to instapaper, and if it's something I wish to check now, I press the shortcut to open it in a new tab, and then I go on. When I'm done, all posts have been marked as read, and then I have a few tabs open that I immediately check out, and a few links in instapaper that I check out later. I never actually read an article or a comic or a video in my reader. It's terrible interface, I find. I much rather check out the actual website. I do the exact same for instapaper; open in a new tab and archive the link.
With the exception of web apps / extensions, it's my understanding that RSS feeds were originally meant to be consumed by a program specifically optimized for handling feeds, instead of a bloated, slow, unsafe web browser.
In the end, your RSS flow could mostly be replaced by a set of live bookmarks in your bookmark toolbar, then you wouldn't even have to leave the browser. Plus you would get easy multi-platform synchronization of your feeds. A hell of a lot easier than running an RSS reader on a private server like a lot of us.
Also, my RSS reader is just a web app, not a native application, so when I get through my list of new posts in my feeds, I'm already in the browser.
The core feature of RSS is that it takes content and moves it from a site the publisher controls and into one the reader controls. This is immensely valuable to readers! It's perhaps less valuable to publishers, however.
Many publishers invest significantly in adding value to and gaining value from their websites. Advertisements, links to other sites, merchandise sales, etc. Almost all of those vanish when you feed only the core content to readers through RSS.
With all that in mind, publishers have ample reason to not invest in RSS. The economics of it are not kind to them.
The only people left using RSS will be the classic web of independent readers and writers, who are still free to donate directly to each other with only a payment processor as middleparty.
At the same time, it's worth considering that those publishers are often much worse off when they escape the cat's malicious paws. More than one newspaper has learned this to their considerable sorrow.