It may be substantially simpler to acknowledge that there is no binding contract involved between me and the supplier of content B. Were this some sort of purchase or legal arrangement that I had consented to in some way, then the content provider would have a much stronger case.

In practice, I arrive at any given site with nothing more than a crude hyperlink and almost no description of the contents. (Maybe I have a search page summary, often I don't. If I do it's usually rather out of date and incomplete.) I cannot trivially know whether content B is present, or what sort of agreement I may or may not be entering into, until data is actually transferred to my device. By that point, I typically already have content B, before I could possibly make an informed choice about whether I wanted to spend my bandwidth downloading it, what cost it may represent, etc.

Technological solutions already exist here. A provider can choose to lock content behind a paywall, communicating an actual cost, and require that I pay it. Providers can also usually quite trivially detect ad blocking technology, and require that I disable it before delivering the content. (At that point, I am making an informed choice!) A provider doing neither of these things has a very weak case imho. I suppose we'll see if the courts agree.

Agree, but the publisher of content A is also the supplier of content B. They are sourced differently on delivery but they are legally delivered as a single piece of "original work" (as this is a law for PC-software, all included libraries in some app are also part of the "original work")

Maybe a case can be made that the work is not shipped in entirety but needs to be assembled at the consumer...?