Say Amazon ceased to exist. In the short term, most of us would experience a drop in sales. Presumably, ardent book buyers would go to other sites. But since most of those sites opened up to self-publishers after Amazon did, not before, presumably as an attempt to blunt one of Amazon's competitive advantages. Would they continue offering self publishing options if Amazon ceased to exist? I'm not at all sure that's the case.
Would it matter? Let's say Amazon goes away. I wouldn't think B&N and similar sites would drop self-publishers. But, let's say they did. Amazon's gone then B&N and Apple drop self-publishers. Would Kobo do so as well? I just don't think so. I think someone is going to try to take advantage of Amazon's absence. But, let's say all the big sites drop self-publishers.
In that scenario, I could see maybe someone like Bookfunnel moving into the void. Plus, all the smaller sites are going to really push to jump into that space.
The Kindle is gone. The Nook is gone. Let's say Kobo too. Are any of the smaller sites going to sell an ereader? Possibly but doubtful. Smartphones, iPads, Android tablets, etc. are all widely available. The smaller sites would probably just build reading apps. They don't need to sell a device when devices are readily available. Now, as they grow, maybe they'll release an eInk reader to fill the gap but who knows.
I imagine a lot of authors will just sell direct from their websites. Before Amazon, non-fiction authors would sell books as PDFs from their sites (or from marketplaces designed for that). Clickbank was (is?) a popular one. Plus it had an affiliate program. Of course, fiction wasn't a big seller that route but don't sites like DriveThruFiction still sell PDFs? And, these days, ePub is a popular option. There are also PDFs sized for mobile. Project Gutenberg, which does public domain books, offers books in HTML5, EPUB3, EPUB and plain text formats. Download or read on their website. You can download and read it in a browser, a reader app that supports epub, or anything that will open a text file. Bottom line is that there are plenty of options. Authors could do the same. Offer epub, PDF and print. Also, you could let people that bought the book read it directly on your site.
People are more accustomed to reading books on their devices than they were 10 or 20 years ago. And now there are more options and choices.
Also, I think "self-publishing" has lost a lot of the vanity press connotations over the past several years, so there is less reluctance to buying self-published books.
So, were Amazon to cease to exist for whatever reason, I believe there'd still be ways for self-publishers to get books to readers.