CORS only applies to requests for restricted resources like fonts or XHR requests that aren't simple GETs and POSTs.
"So, while this is typically not possible: foo.com/index.html ---GET---> bar.com/pic.jpg"
Typically this is possible. Images, stylesheets, scripts, iframes, and videos aren't subject to CORS.
"You can solve it by routing the request through your host server: foo.com/index.html ---GET---> foo.com ---GET---> bar.com/pic.jpg
Not necessary, the client's browser can get bar.com/pic.jpg just fine all by itself.
"Pinning tools like Hashbase and Homebase help keep dat:// sites online"
If you publish a dat archive, how do you notify Hashbase to pin it? Can you do it through dat?
To keep my dat alive with Hashbase, do I have to set up an account, provide and confirm an email address, link a credit card, etc.?
Are centralized servers, financial institutions and surveillance all required components of the anonymous, decentralized, peer-to-peer web?