I can imagine a system where before viewing expensive content (your next ultradeep NYT analysis I really want to read) I'm given a choice to view an ad (video, audio or picture) on one of the topics I'm interested in and be paid say $0.001. There are ad processors, let's say 2 or 3 major ones A, B and C, with whom I have an account. NYT hires one or two of them to give readers reasonable choices of what kind of ads to view and pay both ways. I'm registered with A and C with interests in cars, musical instruments and hiking equipment (in fact they may be priced differently), NYT supports A and B, which is fine, I'll be paid by A this time. I may of course change my preferences over time.
This will make ads even more expensive for the advertisers, but will at the same time improve relevance. In fact advertisers may compete for keywords/interests just like they do with Google Ads.