What we lack, in my opinion, is a form of access control for static websites, such that they are disallowed from making any outgoing requests. The browser is in control of the site code; it should be possible to guarantee that no outgoing requests can take place. As far as I can see, it shouldn’t be difficult, but it’s possible I’m missing something — I assume the difficult part is just reaching agreement.
Perhaps it would be possible to permit outgoing requests where the URL is statically embedded in the HTML (such that the URL cannot depend on form data), thus allowing fetching e.g. remote CSS/JS resources.