Reading cookie-less responses is also forbidden. I couldn't read your Google account information, just make an anonymous Google search through your browser. I fail to see what's the big deal.
Fundamentally this all boils down to you, the person building the site, being cheap. You don't want to pay the handful of dollars to make your own HTTP requests.
I think it's much more about open web and letting the user decide than about being cheap.
Also, one thing I can speculate that phishing would become even easier if such things were allowed