I'm less convinced. Are you saying it's unethical to
automate browsing a site?
Because if you save the pages you browse on some site, they're yours (authors don't own your cache).
Perhaps you're arguing that if you wrote a lightweight script/browser (which is just your user agent) to save some website for offline use, that'd be unethical and GDPR violating? Again, I don't think so but maybe I'm missing something. But perhaps this turns on what defines a "user agent".
Perhaps this becomes a "depth of pre-fetch" question. If your browser prefetches linked pages, that's "automated" downloading, akin to the script approach above. Downloading. To your cache. Which you own. (Where I struggle to see an ethical violation)
Genuinely curious where the line is, or what exactly here is triggering ethics, GDPR and practical standards?