I understand that a common feature like zooming can be complicated enough to be not supported, but why can't the site banner zoom too? If the black top bar can be made screen-fit, and the fact that the reputation and badges disappear when zooming suggests that this particular bar is supported, then why can't the site banner be? There are plenty room for the buttons, and I think the HTML element is basic enough to make it easy.
Before
After
Zoom at 133%
zoom vs resize
are the sameCtrl +
orCtrl -
to zoom it.