Hide the logo in the header of the login screen

I the login screen, we can show/hide the header, which is cool

Sometimes, poeple want the header to be displayed on the login page, but then the logo part of the header mixed with the image added as background of the login page does not render very nicely.

So, the feature request is: When header is not hidden, add "something" (maybe a checkbox?) that allows to hide the its logo, but only in the login page.