Maybe you then run into a social problem: while the PageRank algorithm would dictate to downrank BBC in that case, would the search engine provider actually be

Maybe you then run into a social problem: while the PageRank algorithm would dictate to downrank BBC in that case, would the search engine provider actually be willng to downrank such a popular organization? Think even about places that sperad misinformation and conspiracy theories. Those host poor quality content, but generate traffic so AFAIK don't get penalized in search results.