The internet would change fundamentally. The article lists social networks as things that would disappear, and good riddance, but we'd also lose (free) search engines.
Further, I'd argue that some forms of advertising are actually desirable. If I'm planning a vacation abroad, and want to make a reservation at a hotel, I'd typically go to booking.com or one of it's competitors. Those sites are pretty much 100% advertising, but how else am I gonna find a hotel on the other side of the planet, in a country I've never been before?
You also run into some tricky hairsplitting questions. Where do you draw the line on advertising? Are webshops allowed to list 3rd party products? Or is that advertising? I don't want to outlaw online shopping entirely, it's extremely handy! What about search engine results from those webshops? Free search engines will disappear, but let's say I have a paid account and search for "buy dell laptop". Are the results advertising? How do you differentiate and define the cases legally?
I think it's a good idea, but it's gonna be quite tricky to implement well. And executing this idea poorly is potentially quite bad.
Getting it implemented at all is going to be hard: even well executed, this idea is going to have a huge impact on the economy, and people are not going to like that. This idea would be good for democracy, but ironically democracy is not good for this idea.
I really think people take so much for granted that even when they think about what they take for granted, they still can only scratch the surface.