That's the thing. If you're logged in to good.com (with a session cookie), then go to evil.com and it has an AJAX call to good.com, it'll carry your cookie. Thus - authentication. Suddenly evil.com can remote control good.com. (at least it used to be this way at the time we got CORS; the situation has changed a bit with newer web platform features like SameSite cookie params.)
> The only freedom I want is being able to wget content no differently than from a terminal.
I see your point, I really do. But the Venn diagram overlap of "sites that need to download arbitrary websites", "sites that need to only fetch content client-side in the browser, not via their backend", and "sites that do this for non-nefarious purposes" is infinitesimally small. I'm pretty sure your use case is missing at least one of these three criteria.