Dear Developers!
Please discard this request, as I explored the solution of non-matching size of background image and header image topic.
In the wordpress dasboard > Pages > <selected page> there is a Featured image section at the right panel. If I choose an image over there and I put this selected page for the main slider, the featured image perfectly disappears when I click on a page which has an own header image. So no need for background image. Everybody should use Featured image, instead.
