Indeed. Perhaps a reasonable compromise would be to have the permission apply to only the tab for which the user allowed it, and only as long as the tab remains

Indeed. Perhaps a reasonable compromise would be to have the permission apply to only the tab for which the user allowed it, and only as long as the tab remains pointed to that same domain. No inheriting permissions across child windows and no retaining the permission for that domain when future tabs are opened. Seems like it would reasonably fit the expectations of the user and I can't think it would put up unreasonable road blocks for developers.