While privacy sensitive users may consider this a feature in case of e.g. google.com and youtube.com, the average user is more likely to consider it an annoyance, and worse, it is likely to break some obscure portal somewhere that is never going to be updated, so if one browser does it and another doesn't, the solution will be a hastily hacked note "this doesn't work in X, use Y instead" added to the portal. And no browser vendor wants to be X.
[1] The workaround of using the public suffix list for such purposes is being discouraged by the public suffix list maintainers themselves IIRC, so the "right" thing to do would be breaking Wikipedia.
Edit: If done naively on an origin basis right now, it would break the Internet. You couldn't use _any_ site/app that has login/account management on a separate host name. You couldn't log into your Google account with such a browser anymore (because accounts.google.com != mail.google.com). Countless web sites that require logins would fail, both company-internal portals and public sites.
1) User logs in at google.com/login and sets google.com cookies. 2) Server generates a nonce and redirects to youtube.com/login?auth=$NONCE 3) youtube.com checks the $NONCE and sets youtube.com cookies 4) youtube.com redirects back to google.com.
Firefox's container tabs can maintain isolation despite this since even this redirect will stay within a container. However there is a usability penalty since the user has to open links for sites in the right container (and automatically opening certain sites in certain containers will enable cross-container stapling again).
webapps.stackexchange.com/questions/30254/why-does-gmail-login-go-through-youtube-com
I mean, wouldn't that take care of a whole class of attack vectors and make cross-origin requests possible without having to worry about CSRF?