Other than a completely new approach for producing value such as the 'Freeism' one described in the article suggested in this comment
https://news.ycombinator.com/item?id=20282851 (which I hadn't time to read yet and hence I'm neither in favour of or against) this simply boils down to the questions of who will pay for relevant content and what the business model will be.
By and large, people don't seem to be willing to pay for content on the web. Hence, advertising became the dominant business model for content on the web.
Find another way for someone to pay for relevant content and you can do away with advertising. It's as simple as that.