If users want this, they can just add a tag to their headerinclude. tag can also cause problems, and there's no way to guarantee that adding one automatically on demand won't break things. The compromise could be a global variable initialized by Google SEO but added to headerinclude by the user. That'd be too much effort for a non-existant use case though.
for site/foo/bar/baz/ the 404 page may include missing images due to relative links in the users theme
as there is no other solution, add a <base> tag to the header