"I doubt any of the much smaller niche/hobby or family business type sites I know about would suffer greatly if Google vanished tomorrow either."
Many existing businesses already have awareness built through a variety of channels over a number of years, but if search were to die off some newer sites struggling to build exposure from scratch would struggle harder. That said, as Google keeps lifting the cost barrier to entry & radiates greater risk out to the smaller players perhaps building initially from the perception that Google is perpetually late / behind the curve on new sites, & that one needs exposure elsewhere isn't a bad thing.
"They are often beaten on volume by at least one order of magnitude by a single link from an influential blogger in a relevant field who is genuinely suggesting that their readers visit that site, or the equivalent via Twitter, Facebook, Reddit, Pinterest, etc. And that's before you count the viral effect"
If they don't have an SEO strategy (or are selling a unique product that people don't know exists until they see it) & just let whatever search traffic happen on its own then sure it is easy for other sources to drive vastly more traffic than search. But if they are focused on commercial keywords, build content around the consumer demands their solutions help solve, and have an SEO strategy then search is typically in the top few referrers in terms of revenue driven.
A lot of the top affiliate links on Twitter or such are for iTunes song sales: low cost, low friction & low commitment purchases. I think I have had maybe a couple Twitter conversions in years, while search has driven orders of magnitude more. But both are channels that are part of the awareness process & when you add them together its more like 2+2=5.
"their foundation is still basically the idea that you can judge the worth of a page by how many incoming links it sees"
I think they fold in more usage data than they let on, but feel little need/incentive to mention that aspect of the algorithm.
"I'm reasonably sure that unless they have some shady deals going on with various popular social media sites, they don't even know about probably 90% of the incoming links to most of those little sites I mentioned"
Did you see the bit about using Google Chrome's data saving caching feature on Android? Chrome desktop also has security features baked into it. And there are boatloads of signed in user accounts tied to both of these. And large chunks of many social sites are crawlable.
"All they've got left is the public blogs and the assorted SEO tricksters, and that's not where a lot of people share genuine recommendations any more."
The fact that those votes are harder to give means they (often) have greater discrimination value. It is easy to say that social signals should replace links, but that would effectively be Google subsidizing competing ad networks. And even if we ignored that the "relevancy" signals in social are also the ad units, outside of those official ads there are third party strategies to ensure social is every bit as gamed as the link graph is.
If they don't have an SEO strategy (or are selling a unique product that people don't know exists until they see it)
The second part is what I really had in mind there. One of the sites I was thinking of is a textbook example, a start-up for people who have a certain hobby.
The SEO strategy is reasonably effective: the site consistently ranks on the first page of Google for almost all targeted search terms, which is not a bad achievement starting from a page rank of nothing a few months earlier. But it's partly able to do that because no-one in the field has really done anything similar before, so almost no-one actually searches for anything like it either.
In contrast, more specialised and proactive channels, such as advertising in traditional off-line media or targeting ads at people with that particular interest on social networks, attract very favourable comments and numerically they tend to get far better click-through rates, similar levels of engagement, and in some cases a much higher overall conversion rate/lower CAC.
If you only looked at the hits from Google, your first reaction might quite reasonably be that there was no market for this product, but the feedback once people in the target market actually see it paints a different picture.