Is it redundant to display the search bar on Search Result or Error 404 page again when the website already has it on the sidebar/side navigation or on header?
I've always felt it's kind of redundant since user can easily scroll the page to use the search bar again, but I often see various websites keep employing this. I thought that the search bar is displayed again to prevent the hassle to scroll the page, but I'm still not sure if that's really the reason (especially when it's still on same screen).
Here are some few examples to illustrate:
Sorry for the long question title!