Before computers, television broadcasts defined a "title safe" (or "safe title") area which was a rectangular region in the center of the video signal that any properly maintained television was guaranteed to display. Any words on the screen (titles) should fit within this area which occupies the center 80% of the screen, giving a 10% border all around.
A slightly larger area was the "action safe" (or "safe action") area where a properly maintained television would cut off the image. This area occupied the center 90% of the signal, giving a 5% border. A properly maintained television could display all or none of this area. Only the title safe area was guaranteed to be visible.
You asked whether there were any "computers that did not limit their display to a box centered in the middle of the screen". I think you are referring to the title safe area, and the answer is yes. The Commodore 64 and other computers could set the color of the border outside of the title safe area and could display sprites in this area. The NES went a step further by displaying a 256×240 pixel picture that covered the whole action safe area, and within that the center 224×192 pixels were considered to be title safe."
Computers used for full screen video production such as the Commodore Amiga (1985) also needed to be able to write to the entire action safe area. See Bruce Abbott's answer for more information.
So two use cases for this ability arewere (1) games, and (2) video.
In place of analog electron guns that had to be adjusted to keep the picture centered and sized correctly, today's digital displays have hardware pixels that go right up to the viewable edge of the screen and so the entire video signal is both action safe and title safe.