Some very quick thoughts.
From a privacy perspective, using some limited data from sites {A,B,C} to advertise on site D could be fine *if* D doesn't actually learn anything and the person can never be recognised across contexts at all. Some form of opaque reusable SDA.
From a strategic perspective, the fact that data from one context can be used in another isn't just a privacy problem, it's really bad for publishers too when they can't control what other contexts and purposes it gets reused in.
Right now the model is that pubs just give up data and intermediaries can do whatever they want. This has strong anticompetitive dynamics and is key to eg. Google's dominance. It's also key to the financing of crap and disinformation.
The whole "financing the open web" discourse is really a way of saying that high quality publishers should be subsidising low quality ones so that intermediaries can get rich. That model has negative social value.
But publishers could still have forms of solidarity and cooperation! For that to work, however, they would have to pick who they want to work with, have some solid ground rules, and be in a position to enforce against violators.
Anyway — I don't think your idea is crazy! It may be hard to make work, but it's not crazy. What's crazy is that the "open web" adtech CEOs are claiming to be hardcore redistribution socialists and no one thinks that's suspicious.