I have been thinking about the same problem since a few weeks. The real problem with search engines is the fact that so many websites have hacked SEO that there is no meritocracy left. Results are not sorted based on relevance or quality but by SEO experts' efforts at making the search results favor themselves. I can possibly not find anything deep enough about any topic by searching on Google anymore. It's just surf…
The first, and the most important perhaps was page load speed. We adopted a slightly more complicated pipeline on the server side, reduced the amount of JS required by the page, and made page loading faster. That improved both the ranking and actual usability.
The second was that SEO people told us our homepage contained too many graphics and too few text, so search engines didn't quite extract as much content from our pages. We responded by adding more text in addition to the fancy eye-catching graphics. That improved both the ranking and actual accessibility of the site.