Browsers need a "keep my cookies" button next to the url bar, separate cookie jar per domain, and then by default, delete all the cookies when you close the window. No EU cookie prompts would be needed, no "this feature does not work without third party cookies, no DNT, no nothing... silently accept all the cookies, and then delete them. (and other persistent storage too).

Want to stay logged in? Press the "keep the cookies for this domain" button by the url bar, and a separate cookie jar will be made just for example.org and persist there.