Where would these backlink farms get their reputable backlinks from to make this work though?

It's not like e.g. the BBC are going to start linking to AI generated articles without checking their accuracy. And if they did, the BBC would risk their PageRank influence and their own ranking.

I get backlink farms can work right now and Google doesn't strictly follow PageRank, but I'm asking if the PageRank concept used in the right way would help.

Probably from buying up expired domain names that used to host reputable content and that have earned links in the past.

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.