That's exactly why I said you don't understand what targeted advertisement can do. Let's talk about 3 concepts:
1) Relevance. Take your cooking website example, say if that recipes has chicken in it. Then the magazine method can show you an ad about local supermarket for you to buy chicken. Then how do they know if you "probably" prefer walmart or wholefoods or local farmer's market? What if you are an organic guy? (which means you probably prefer wholefoods) Traditional magazine method doesn't make the result relevant enough for today's online advertising standard.
2) Feedback. As a brand who wanna do an online campaign, how do I know if my advertisement works? Today's advertiser no longer count on clicks, they count on impression. They don't need you to click to ad. They just want to make sure you see it. How do they if you didn't block to ad? How do they know if you didn't go to other tabs when their 15 second youtube ad is playing? That means at least 1 additional request send out from your browser. Usually it's more because they wanna know if you watched half of the video or the whole video. Things above don't have to be done with tracking you profile, but the other things does. For example, how to the advertisers know if they reach their target audience? If I'm selling the new mustang how do I know if I show the ad to ford people instead of chevy people? It's called on target percentage and it's one of the top metrics advertisers care about.
3) Availability. In many situations, there's just no ad available that actually relevant to the content. Then it's better for advertisers to show you something that may relevant to you instead of something completely random or no ad at all.
Your magazine method has works for decades doesn't mean it will continue to work in the future. Does magazine itself still work?
BTW, when I raise the WSJ thing I didn't target you specifically and I have no idea you had that comment you posted before. But as you said, you (and probably most people) won't pay for subscription for such ridiculous publication. Then advertisement is the way for you to read it freely so you can identify if the article is ridiculous or not. Or maybe just don't read it and comment by title?