If you change your browser's UserAgent string to Googlebot, then your client will be treated as a first-class citizen, by many of these sites. Google always wins, so let's all be Google.
If only they all did this. So many sites I get to and they're a blank page or an absolute disaster....
Update those periodically (hours / days / weeks). The adverts don't change particularly quickly.
On the flip side, some people can't change their IP addresses easily, and getting IP banned (even if rare because of the reasons you stated) is actually a major hassle when it actually happens for those people. :/
However, I don't see cache links on Google :(
Edit: Oops, I'm wrong. The article does say that the Google bot only sees the first paragraph or so.
"The reason: Google search results are based on an algorithm that scans the internet for free content. After the Journal’s free articles went behind a paywall, Google’s bot only saw the first few paragraphs and started ranking them lower, limiting the Journal’s viewership."
So maybe this is why there's no Google cache.
Also, if Google can only index the first few paragraphs, the results are much less comprehensive.