What is your definition of "useful"?
Look, I agree that the on page optimization focus should be keyword related content, well defined navigation structure, and all that. But no matter what line of flowery prose Google spouts about designing web sites for people and whatever other mantra they are spouting, the Google algorithm is weighted on links. Specifically it is weighted on inbound links from trusted web sites. Period. The End.
Of course, that's what makes Google the best search engine, because it doesn't rely on the website builder to tell them how good their site is, it relies on other people 'voting' for it with links.
I don't put much weight or reliance on on-page factors, it takes 15 seconds to optimise a page for a keyword (assuming the page is already about that subject) so let's assume relevance to the search is a given and that google is now trying to decide where that page should rank out of all the pages it found on the search subject.
It mostly looks at those links from the trusted sites like you said. Getting those links is damn hard, unless of course you can provide something that's useful to that trusted site's visitors so that the site owner givers his own users a way to leave his site and go somewhere else. It's a beautifully simple model and the best way to replicate it is genuinely.
What is your definition of "useful"?
It's not my definition that matters, it's Google's, but it's a hugely important concept to understand I think, in SEO. It's almost so obvious that you don't think about it, when in fact it drives the ranking algo and is the correct perspective to look at SEO from IMHO....
Google want their index to be useful to people right? Or people won't use Google anymore. Google can't directly influence the content of their index, they don't build the sites, but what they can do is tell us what they want to see and give us tools to help us achieve that. They've had a
massive influence on how modern websites are structured. In that respect they appear to support SEO when in fact the oposite is true, they wnat us to build properly structured websites then let nature take it's course, but by telling us a few things about how to rank well (although they never word it like that of course), they get a better quality of site.... hopefully.